Solve the equation and also check your results:(1-2x)/7 – (2-3x)/8

1.	Solve the equation and also check your results:(1-2x)/7 – (2-3x)/8 = 3/2 + x/4
Answer» (1-2x)/7 – (2-3x)/8 = 3/2 + x/4 Let us rearrange the equation (1-2x)/7 – (2-3x)/8 – x/4 = 3/2 By taking LCM for 7, 8 and 4 which is 56 ((1-2x)8 – (2-3x)7 – 14x)/56 = 3/2 (8 – 16x – 14 + 21x – 14x)/56 = 3/2 (-9x – 6)/56 = 3/2 By cross-multiplying 2(-9x-6) = 3(56) -18x – 12 = 168 -18x = 168+12 -18x = 180 x = 180/-18 x = -10 Let us verify the given equation now, (1-2x)/7 – (2-3x)/8 = 3/2 + x/4 By substituting the value of ‘x’ we get, (1-2(-10))/7 – (2-3(-10))/8 = 3/2 + (-10)/4 (1+20)/7 – (2+30)/8 = 3/2 – 5/2 21/7 – 32/8 = 3/2 – 5/2 3 – 4 = -2/2 -1 = -1 Hence, the given equation is verified.

Solve the equation and also check your results:(1-2x)/7 – (2-3x)/8 = 3/2 + x/4

Answer»

(1-2x)/7 – (2-3x)/8 = 3/2 + x/4

Let us rearrange the equation

(1-2x)/7 – (2-3x)/8 – x/4 = 3/2

By taking LCM for 7, 8 and 4 which is 56

((1-2x)8 – (2-3x)7 – 14x)/56 = 3/2

(8 – 16x – 14 + 21x – 14x)/56 = 3/2

(-9x – 6)/56 = 3/2

By cross-multiplying

2(-9x-6) = 3(56)

-18x – 12 = 168

-18x = 168+12

-18x = 180

x = 180/-18

x = -10

Let us verify the given equation now,

(1-2x)/7 – (2-3x)/8 = 3/2 + x/4

By substituting the value of ‘x’ we get,

(1-2(-10))/7 – (2-3(-10))/8 = 3/2 + (-10)/4

(1+20)/7 – (2+30)/8 = 3/2 – 5/2

21/7 – 32/8 = 3/2 – 5/2

3 – 4 = -2/2

-1 = -1

Hence, the given equation is verified.