# Mathematics Questions and Answers – Reduce the Given Linear Equations to a Simpler Form

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This set of Mathematics Question Bank for Class 8 focuses on “Reduce the Given Linear Equations to a Simpler Form”.

1. Solve: $$\frac{3x+7}{12} + \frac{22x-1}{3}$$ = 1.
a) $$\frac{9}{91}$$
b) $$\frac{27}{273}$$
c) $$\frac{-27}{273}$$
d) $$\frac{-9}{91}$$

Explanation: $$\frac{3x+7}{12} + \frac{22x-1}{3}$$ = 1
∴ $$\frac{3*(3x+7)+12*(22x-1)}{12*3}$$ = 1
∴ 9x + 21 + 264x – 12 = 36
∴ 273x + 9 = 36
∴ 273x = 27
∴ x = $$\frac{27}{273} = \frac{9}{91}$$.

2. Simplify: $$\frac{2x+1}{2} + \frac{2x-1}{3}$$ = 1.
a) 10x = 5
b) 5x = 10
c) 10x + 5 = 0
d) 5x + 10 = 0

Explanation: $$\frac{2x+1}{2} + \frac{2x-1}{3}$$ = 1
∴ $$\frac{3*(2x+1)+2*(2x-1)}{6}$$ = 1
∴ $$\frac{6x+3+4x-2}{6}$$ = 1
∴ 6x + 3 + 4x – 2 = 6
∴ 10x + 1 = 6
∴ 10x = 5

3. Solve: 11x – 2 = 7x + 12.
a) –$$\frac{7}{2}$$
b) $$\frac{7}{2}$$
c) $$\frac{14}{2}$$
d) $$\frac{14}{6}$$

Explanation: 11x – 2 = 7x + 12
∴ 11x – 7x = 12 + 2
∴ 4x = 14
∴ x = $$\frac{14}{4} = \frac{7}{2}$$.
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4. When the equation $$\frac{12x}{2} + \frac{6x}{5}$$ = 0 is simplified the solution of the equation would be?
a) x=0
b) x=1
c) x-1=0
d) x+1=0

Explanation: $$\frac{12x}{2} + \frac{6x}{5}$$ = 0
∴ $$\frac{5*12x}{2*5} + \frac{2*6x}{5*2)}$$ = 0
∴ 60x+12x=0
∴ 72x=0
∴ x=0.

5. Solve: 12x-13=2x*(11-12).
a) x+$$\frac{13}{14}$$=0
b) x-$$\frac{14}{13}$$=0
c) x=$$\frac{13}{14}$$
d) x+$$\frac{14}{13}$$=0

Explanation: 12x-13=2x*(11-12)
∴ 12x-13=22x-24x
∴ 12x-13= -2x
∴ 14x=13
∴ x=$$\frac{13}{14}$$.

6. Simplify: $$\frac{13x-1}{12}$$=12.
a) x=$$\frac{13}{145}$$
b) 13x+145=0
c) 13x=145
d) 145x+13=0

Explanation: $$\frac{13x-1}{12}$$=12
∴ 13x-1=144
∴ 13x=145
∴ x=$$\frac{145}{13}$$.

7. Simplify: t – 12 = 12t – 1.
a) 1+t=0
b) 1-t=0
c) t+1=0
d) t=0

Explanation: t – 12 = 12t – 1.
∴ -11t=11
∴ t=1.

8. Solve: 13x-2=21x+2.
a) 2x+1=0
b) 2x-1= 0
c) 1 + 2x = 0
d) 1 – 2x = 0

Explanation: 13x-2=21x+2
∴ 13x-21x=2+2
∴ -8x=4
∴ x=$$\frac{-1}{2}$$.

9. What will be the solution for equation 3j+2=1-3j.
a) $$\frac{-1}{6}$$
b) $$\frac{1}{6}$$
c) $$\frac{1}{12}$$
d) $$\frac{-1}{12}$$

Explanation: 3j+2=1-3j
∴ 3j+3j=1-2
∴ 6j=-1
∴ j=$$\frac{-1}{6}$$.

10. Solve: 12x+2=13x-1.
a) 1
b) 2
c) 3
d) 4

Explanation: 12x+2=13x-1
∴ 12x-13x=-1-2
∴ –x=-3
∴ x=3.

Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

To practice Mathematics Question Bank for Class 8, here is complete set of 1000+ Multiple Choice Questions and Answers.