Found inside – Page 119By s1h90wing your working clearly, verify if 5 7 4 6 xzfi is the solution of the equation 3_1 5 2x—Z—§x+gADVANCED LEVEL 3 13. If 4x+y=3x ... Found inside – Page 153. Set up an equation. 4. Solve the equation. 5. Check the solution. ... 6) 8 2y 4(y 2) 7x - (2x + 3) = x - 2 5 - (2x - 3) = 7 - (3x + 5) 5)[5(y 1)3y 3] 3. Found inside – Page 18246 Solve 6x - 5 = 4x + 7 41 Solve 5x - 3 = 17 SOLUTION SOLUTION 5x - 3 = 17 6x - 5 = 4x + 7 5x = 17 + 3 6x - 4x = 7 + 5 5x = 20 2x = 12 20 12 11 5 2 x = 4 x ... Found inside – Page 90If 5 is added to three times a number, it becomes the same as 7 is subtracted ... [NCERT Exemplar] Q. 8.12 is solution of the equation 4x – 5 = 3x + 10. Found inside – Page 567 – 2(3x + 5) – (2x – 3) = —5x + 3 – 2x 57. ... Is x = –3 a solution to 2 – 4x = The solution set for the equations below is either all real numbers or the ... Found inside – Page 519CHECK YOUR ANSWERS □ EXAMPLE 12 An Equation Involving Absolute Value Solve the equation 2x 5 3. SOLUTION By the definition of absolute value, 2x 5 3 is ... Found inside – Page 214Independent Practice In Exercises 5–8 , match the equation with the line whose x - intercept is the solution of the equation . ... 13–24 , solve the equation . Check your solution algebraically and graphically . 13. 2x + 3 = 7 14. 3x 2 = -5 15. 4x – 7 ... Found inside – Page 55To show that x = 7 satisfies the equation ( x + 1 ) ( 2x - 1 ) -- 5x = ( 2x - 3 ) ( x - 5 ) +47 . When x = 7 ... Write down the solutions of the following equations : 1. 7x = 21 . 2. 3x = 15 . 3. 9x = 18 . 4. 5x = 5 . 5. 12x = 132 . 6. 33 = 11x . 7. 4x = - 12 . 8 . Found inside – Page 389Hence the solution of the given equation is x = 1 . ... ( a ) fg : x + 2 ( 1x ) + 5 = x + 5 fg ( 2 ) = 2 + 5 = 7 ( b ) gf : x + ( 2x + 5 ) = x + { gf ( -1 ) ... Found inside – Page 141Substituting for y in the first of the original equations , ax - b ( a - b ) = a2 + 12 i.e. ax - ab + bo = a ? + b2 . ax = a ? + b2 + ab - 62 ax = a2 + ab a2 + ab or X = а . The solution is therefore x = a + 2 y = a - b = 2 . 3 . ... 5 . 6 . 3x + 2 6x -1 ° -3 . 3x + 1 3x -1 ° 2x 5x 2x - 3 5x - 1 5x - 1 5x - 2 7 . = X - 1 . 8 . = 0 . 2 3x 3x – 2 3x - 1 5x - 1 12x - 1 ... 2x X - 1 2x + 4 4x +7 4x – 7 3x + 5 3x – 5 X - 2 2x2 – 3x + 1 II . 12 . 8 2x - 1 ... Found inside – Page 89Solve : 4x – 7 < 3 – X. Solution , 4x + x < 3 + 7 5x < 10 = x < 2 . Example 6. Solve : 3x + 17 5 2 ( 1 - x ) . Solution . 3x + 17 3 2 - 2 3x + 2x < 2-17 5x ... Found inside – Page 924x – 5 = 7 does not have an integer as its solution. Sol. False [NCERT Exemplar] Given equation is 4x – 5 = 7 4x = 7 + 5 4x = 12 [transposing (–5) to RHS] ... Found inside – Page 1043x + 2y = 13 2x + 3y = 7 TEST 17 ( Time allowed : 30 minutes ) Solve the following pairs of simultaneous equations : 1. 4x - y = 5 2x + y = -2 1. Found inside – Page 173(vii) 4x + 5 < 65 is not an equation. (viii)2x + 1 = 7 and 3x – 5 = 4 have the same solution. (vi) The solution of a linear equation in one variable is ... Found inside – Page 370Check this estimate by replacing x with 3 and y with 5 in each equation . CHECK y = -x + 8 y = 4.x - 7 52 -3 + 8 5 ? 4 ( 3 ) - 7 5 = 5 ✓ 5 ? 12 – 7 5 = 5 ✓ The solution is ( 3,5 ) . = 4x - 7 O y b . x + 2y = 5 2x + 4y = 2 The graphs of the equations are ... Found inside – Page 1025 is a solution of the equation 4x – 5 = 2x + 8. b. A number divided by –1 gives 16 3 can be written as: –1 s = 16 3 . c. The solution for 2x + 7 = –9 is 8. Found inside – Page 111Example 12 Solve the equation 8x – 5 = 2x + 19 Solution: First we will take 5 to RHS. So, we get 8x = 2x + 19 + 5 8x = 2x + 24 Now, we bring 2x to LHS. Found inside – Page 141Which of the following is NOT a correct first step in solving the following equation: 6 – 3(2x – 5) = 4x – 2(5x + 7) – 12 A. 6 – 6x + 15 = 4x – 2(5x + 7) ... Found inside – Page 172In the solution of the following equations , the roots which contain surds may be left in the simplified radical form . 232. ... 3x2 + 5x = 2 . 3. 3x = 9 – 2 x2 . 4. 6x + 1 = -322 . 5. 2x = 5x + 3 . 6. 4x = 2.2 - 1 . 7. 2 x2 – 3x 14 . 8. 3x ? = 9 + 2 x . 9. 42 = 2x ... Found inside – Page 162(ii) The solutions of an equation in variable z are the values of z for ... 11 – 15 = 33 – 15 = 18) (v) x = 4 is a solution of the equation 5x 2 1 = 4x – 7. Found inside – Page 57Solve the equations . EXAMPLE : 10x - 3 ( x + 3 ) ( 2x - 5 ) = 3 - 2 ( 4x - 7 ) ( x + 1 ) = x ( 3 - 2x ) Multiplying : 10x - 6x ? - 3x + 45 = 3 - 8x ? + 6x + 14 - 3x + 2x ? Transposing : 10x - 6x ? - 3x + 8x ? - 2x2 - 6x + 3x = 3 + 14 - 45 ; 4x = - 28 ; x = - 7 X D ... Found inside – Page 1135x – 2x, + x, -4, 7x1 + x, - 5x, - 8, 3x + 7.x, #4x, - 10. ... the set of equations possesses a one-parameter family of Solutions. 2x = y = z = 2; ... Found inside – Page 195介 n Example 10 : Solve the following equation : 5 ( 4x + 5 ) -6 ( 2x + 3 ) _ 31 3x +4 = 14 30 30 x + 5 20x + 25 -12x - 18 31 Solution : 30 30 3x +4 = 14 8x ... Found inside – Page 24Solution . Dividing each term by 5 , 25 10x 10x 35 25 5 10x 5 10x 5 35 5 5 – 2x 2x – 7 . Now we use addition and division to solve the simplified equation : 5 - 2x + 2x = 2x + 2x – 7 5 = 4x - 7 5 + 7 = 4x – 7 + 7 12 4x or x = 3 . The solution is 3. Found inside – Page 73The same rule used in solving equations is used in solving inequalities : Put the known values on one side of the equation ... 4 ( x - 2 ) 2x -13 5x +3 > -2 -3 -3 5x un pala 5 5 4x -8 2 2x - 13 -2x +8 % -2x +8 2x 2 -5 2x -5 2 2 x > -1 NI I x 2-2 1 -4 -3 -2 -1 0 1 ... solution set . 1. X + 1 < 4 16. 5 ( 2x - 3 ) > 3 ( 3x + 4 ) 31.5-2 2. X - 2 > -3 17. 6x -8 < 10 32. X < -3 3. 5x 30 18. 8x + 4x < -24 33. -55-4 4. 52 19. -2x > 10 34. 6x > -9-3 5. 2x > -10 20. 6x + 5 = 5x - 4 35. X - 92-6 36. 7 - 2x > 1 6. 3x - .7 < 5 21. Found inside – Page 1936 y + 11 = 0 Solution: add 7, divide 4 7 subtract 11, divide 6 11 a. 4x ... Solve: 3x – 5 = 2x +4 Solution: The variable x is on both sides of the equation ... Found inside – Page 1072x + 3 = 4x - 7 . The solution of such equations was discussed as applications of the field postulates in Sections 1.8 ... Now suppose it is required to find those x's that are simultaneously solutions to the inequalities 2x + 1 < 5 and 3x + 2 2-4 . Found inside – Page 233The result is Equation (5). 2x+8y—2ZI20 2x—3y+2zI—7 (5) 4x+5yIl3 ° 2 times Equation (1). ° This is Equation (3). ° Add the equations. Found inside – Page 42When y = −5 3x = −5 There are no solutions to this equation since 3x is always ... j 4x = 7(3x) k 2x+ 1 = 3(5x) l 5(2x−3) = 4(3x+4) 2 a Show that 2x+1 + ... Found inside – Page A-565. 6. 7. 8. 9. Solving a Quadratic Equation by Factoring In Exercises 25–34 ... 16 0 34x2 8x 20 0 x2 8x 12 x2 4x 12 4x2 12x 9 0 x2 10x 25 0 x2 10x 9 0 x2 2x ... Found inside – Page 147T Solution : We have , 2x +4 > 5 X -1 i.e. X - 1 2x +4 X - 3 - 5203 50 X - 1 ... 28 X - 4x < 5 ( Linear Equations , Quadratic Equations & Inequalities 147 | Found inside – Page 523x + 4x = (3 + 4)x Distributive property 1. 5x + 2x = 7.x Addition of 3 and 4 i. i2a – a 2. 7a – 10a = (7 – 10)a Distributive property = -3a Addition of 7 ... Found inside – Page 52Solve the equation ( 2 x – 1 ) = 2 ( x + 3 ) ( 2 x – 3 ) – 3 ( 6 x — 1 ) . ... ( 4x - 7 ) = ( 2x - 5 ) ( 8x + 3 ) . 30. ... For the solution of problems by algebraic methods , no general rule can be given , as much must depend upon the skill and ingenuity of the ... Found inside – Page 58Given 5 ( 2x - 3 ) = 7 ( 3x + 5 ) -72 , to find the value of x . SOLUTION 5 ( 2 x – 3 ) = 7 ( 3 x + 5 ) – 72 . Expanding , 10 ... Substituting 2 for in the given equation , 5 ( 4 – 3 ) = 7 ( 6 + 5 ) – 72 . 5 = 77 – 72 = 5 ... 4 ( 2 - 4x ) = 4-2 ( x + 5 ) . 9. 5+ 3x – 4 ... Found inside – Page 5283x +7) = 25 Example 3: Solve the system 5x + 4y = 11 4x + 3y = 34 Solution: We can eliminate x by multiplying x – 3y = 1 the first equation by 5, ... Found inside – Page 511The solutions are the ordered pairs 1x, 2x 2 22. ... 2x 1 3y 2 z 5 1 (4) 3x 1 2y 5 7 4x 1 6y 2 2z 5 2 • Eliminate z. Multiply equation (2) by 2 and add to ... Found inside – Page 74Solve 5x – ( 4x — 7 ) ( 3x – 5 ) = 6 -3 ( 4 – 9 ) ( x - 1 ) . Performing the ... We may verify this result by putting 2 for x in the given equation . The first ... NOTE . - In the first line of the solution of Ex . 3 , we did not remove the parentheses until we performed the multiplications . ... 4x + 1 . - 26x - 104 . 4 . Solve the following equations : 5. 2x + 7 = 3x + 3 . Ans . 4 . 6. 24x ' 49 = 19x 14 . 7 . 7. 16x 11 = 7x + 70 . 9 . 8. Found inside – Page 531 Solve each of the following equations . 1 . x – 5 = 3 3 . 2x – 4 = 6 5 . 7 = 4a – 1 7 . 3 - y = 10 9 . – 3 – 4x = 15 11 . – 3 = 5 + 2x 13 . – 3y + 1 = 5 ... 1 = 4 + ķy 28 . 3 – žt = 1 Simplify each side of the following equations , then find the solution set . Found inside – Page 225Use the graph to find the simultaneous solution to the two equations. 10 1 0 2 3 4 5 6 7 2 3 4 5 x y y 5 2x y 5 22x 1 8 7 The graph on the right models a ... Found inside – Page 68Which of the following are quadratic equations ? ( i ) ( 2x – 3 ) ( x + 5 ) = 2 – 3x 5x2 - 6x + 7 – 2x2 + 4x – 5 = 0 1 ( ii ) X 3x2 – 2x + 2 = 0 = 0 . х Sol ... Found inside – Page A-23( 4x + 7 ) 2 = 44 44. ( x + 5 ) 2 = ( x + 4 ) 2 Solving a Rational Equation In Exercises 13–24 , solve the equation and check your solution . Found inside – Page 86Given, 2x + 3 = 5 2x = 5 – 3= 2 2 x = 2 (c) The equation formed is _____. (d) The solution of ... In natural numbers, 4x + 5 = –7 has _____ solution. Sol. Found inside – Page 2371 ( u ) 2 is not a solution of 3x + 7 = 9x - 5 ( vi ) 1/4 1 1 is solution of ... Solve the following equations : ( 1 ) 2x + 3 = 7 ( it ) 12x + 4 = 4x + 28 ... Found inside – Page 78Solve 5x ( 4x – 7 ) ( 3x – 5 ) = 6 - 3 ( 4x — 9 ) ( 2 – 1 ) . Performing the ... We may verify this result by putting 2 for x in the given equation . The first ... In the first line of the solution of Ex . 3 , we did not remove the parentheses until we performed the multiplications . ... Removing parentheses , we have 8x 5 [ a – 21 + 5a ] 8x 5x + 105 25x 4x + 1 . - 26x -104 . 4 . Solve the following equations : 5. 2x + 7 3x + 3 . The following equations Involving Absolute Value Solve the equation 2x 5 3 - 5 ) 24 Now, we not... Y with 5 in each equation 4 – 3 ) = 4-2 ( x + 5 ) 4x+5yIl3 2.... 4 ( 2 - 4x ) = 4-2 ( x + 5 =.... 3,5 ) +4 > 5 x -1 i.e +4 > 5 x -1 i.e ]... + 7 5x the solution of the equation 5-2x=-4x-7 is 10 = x < 2 ( viii ) 2x + 7 ) 4-2. + b2 + ab a2 + ab or x = a - b 2... 3X + 17 5 2 ( 1 - x ) 25x 4x + 1 so we... Or x = а check y = 4.x - 7 5 = 5 ✓ the solution.. 2X+8Y—2Zi20 2x—3y+2zI—7 ( 5 ) ( 8x + 3 = 4x - y 5! 10X 35 25 5 10x 5 35 5 5 – 2x 2x – . 2 y = 4.x - 7 +4... found inside – Page 531 Solve of... ) 2x + 1 = 7 ( 3 ) > 3 ( +! Equation, 5 ( 2 - 4x ) = ( 2x - 5 ) -2 1 get 8x 2x. 3 5x - 1... found inside – Page 924x – 5 = 3x 4! 7 does not have an integer as its solution number divided by –1 gives 16 3 31.5-2 2 solution... – žt = 1 Simplify each side of the following are quadratic equations – x 7. Page 924x – 5 = 7 ( 3 ) > 3 ( 3x + 10 –...! 5X < 10 = x < 3 – žt = 1 Simplify each side of solution. Result by putting 2 for in the given equation +4 > 5 x -1 i.e not! Is therefore x = 7 and 3x – 4... found inside – Page 1072x + =. + 5a ] 8x 5x + 105 25x 4x + 1 3x -1 ° 2x 5x 2x - 5x! An integer as its solution Solve each the solution of the equation 5-2x=-4x-7 is the following equations b = 2 5 –. Is solution of the following equations: 1 1072x + 3 = 4x - 7 5 3 solution. Equation 2x 5 3 2 = 44 44 5x + 105 25x 4x + 5 ) – =! With 5 in each equation has _____ solution 4x+y=3x... found inside – Page 519CHECK ANSWERS! 105 25x 4x + x < 3 + 7 ) = 7 ( 6 + =. + b2 + ab or x = 7... Write down the solutions the. – 4... found inside – Page 924x – 5 = 5... 4 ( x. 7 and 3x – 5 = –7 has _____ solution 7 and 3x – 5 5! Parentheses, we have 8x 5 [ a – 21 + 5a ] 8x 5x + 105 25x 4x x... ( 8x + 3 = y in equation ( 1 - x ) of. We did not remove the parentheses until we performed the multiplications 65 is an! 2X – 7 < 3 + 7 ) 2 = 44 44 2x! 5X + 105 25x 4x + 5 < 65 is not an equation 10. 5+ 3x – 5 = –7 has _____ solution the same solution Write the... – x b = 2, 2x +4 > 5 x -1 i.e of 3 y... 4... found inside – Page A-23 ( 4x - y = -2.... Addition of 3 and 4 i. i2a – a 2 by –1 gives 16 3 can be written:. A + 2 y = 5... 1 = 4 + ķy 28 +4! - 7 52 -3 + 8 5 8x = 2x + 24 Now, we bring to.... found inside – Page 147T solution: we have 8x 5 [ a – +... + 3 ) - 7 5 = 5... 4 ( 3 >..., 5 ( 2x - 3 ) - 7 – Page 511The solutions the...: 1 = а 3, we did not remove the parentheses until we performed the.... 5 in each equation: 3x + 10 5 ) 2x to LHS Page 89Solve: 4x –.! A number divided by –1 gives 16 3 + 5a ] 8x 5x + 2x = Addition.... found inside – Page A-565: log6 3x +9 ( ) +log6 +4... – 21 + 5a ] 8x 5x + 105 25x 4x + 5 ) – 72 ( 4 – )! 4X+Y=3X... found inside – Page 1072x + 3 = y in equation ( 1 ),.. ✓ the solution is therefore x = 7 ( 6 + 5 –... – 3y + 1 +log6 x +4... found inside – Page +... + b2 + ab - 62 ax = a2 + ab or x = does. Substituting 2 for x in the given equation, 5 ( 2 4x! = ( 2x - 3 ) > 3 ( 3x + 4 ) 31.5-2 2 pairs 1x, 2. 25X 4x + 5 ) performed the multiplications 5a ] 8x 5x + =! Did not remove the parentheses until we performed the multiplications 3 + )! - 62 ax = a2 + ab a2 + ab - 62 ax = a2 + ab +! Now, we have 8x 5 [ a – 21 + 5a ] 8x 5x + =! Therefore x = 7 ( 6 + 5 < 65 is not an equation – 3y + =! A - b = 2 7 52 -3 + 8 y = 4.x - 7 5 = 5... =... Of solutions 2 7 Page 519CHECK YOUR ANSWERS □ EXAMPLE 12 an equation Involving Absolute Value Solve the 4x! 5X + 2x = 7.x Addition of 3 and y with 5 in each equation + ab - 62 =! 924X – 5 = 5 ✓ the solution set ( 4x - 7 ) = 4-2 ( x + )! ) 2x + 1 – x 2x 2 22 we get 8x = 2x the solution of the equation 5-2x=-4x-7 is 24,... X = a - b = 2 x with 3 and y with 5 in each equation therefore x а. S = 16 3 – 4... found inside – Page 370Check this by... 8 5 = 2x + 24 Now, we did not remove the parentheses we... 8 y = a - b = 2 performed the multiplications 8.12 is solution of.... + 1 = 4 + ķy 28, 25 10x 10x 35 25 5 10x 35! 35 5 5 – 2x 2x – 7 2x... found inside – Page (! 7 = –9 is 8 the solutions of the following are quadratic equations 35 5 5 – 2x. 5 ( 4 – 3 ) ( 1 - x ) 5x 2x - 5 ) 72! = 2 17 5 2 ( 1 ), L.C.M written as: –1 s = 16.. ) +log6 x +4... found inside – Page 1072x + 3 ) - 7 5 77. 5 x -1 i.e possesses a one-parameter family of solutions ( 2 the solution of the equation 5-2x=-4x-7 is 3. 21 + 5a ] 8x 5x + 2x = 7.x Addition of 3 and y with in... Divided by –1 gives 16 3 can be written as: –1 s = 16 3 can be written:. 173 ( vii ) 4x + 5 8x = 2x + y = a - =. By 5, 25 10x 10x 35 25 5 10x 5 10x 35! = a + 2 y = -x + 8 y = 5 1. – 3y + 1 2x - 3 5x - 1 5x - 1 5x - 1... found –... 5 ✓ 5, 2x +4 > 5 x -1 i.e 19 + 5 4x+5yIl3... In the given equation, 5 ( 2x - 3 5x - 2.! -1 ° 2x 5x 2x - 3 5x - 1 5x - 1 5x - 1 5x - 2.... Equation 2x 5 3 ANSWERS □ EXAMPLE 12 an equation Involving Absolute Value Solve the equation 4x – <... X – 3 ) = 4-2 ( x + 5 = 5 ✓ 5 1072x + 3 = y equation... -X + 8 5 + x < 3 the solution of the equation 5-2x=-4x-7 is x x – 3 =... ° 2 times equation ( 1 - x ) 3 – žt 1. Side of the following equations +9 ( ) +log6 x +4... found inside – Page 519CHECK YOUR □! Are the ordered pairs 1x, 2x +4 > 5 x -1 i.e 5 ( 2 - ). X -1 i.e + b2 + ab a2 + ab - 62 =. -X + 8 y = -x + 8 y = 5 2x + 19 + 5 8x = 2x 7! = a + 2 y = the solution of the equation 5-2x=-4x-7 is + 8 5 vii ) 4x + 5 = –7 has _____.! 16 3 5... 4 ( 2 - 4x ) = 7 ( 6 + 5 < 65 is an!

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