# Mathematics Questions and Answers – Reduce the Linear Equation and Find the Value of the Variable

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Reduce the Linear Equation and Find the Value of the Variable”.

1. Solve: $$\frac{2x-11}{2} + \frac{x}{7}$$ = 5.
a) x = $$\frac{147}{16}$$
b) x = $$\frac{16}{147}$$
c) x = $$\frac{14}{167}$$
d) x = $$\frac{167}{14}$$

Explanation: $$\frac{2x-11}{2} + \frac{x}{7}$$ = 5
∴$$\frac{7*(2x-11)}{7*2} + \frac{2*x}{2*7}$$ = 5
∴$$\frac{14x-77+2x}{14}$$ = 5
∴16x – 77 = 5 * 14
∴16x – 77 = 70
∴16x = 147
∴x = $$\frac{147}{16}$$.

2. Solve: $$\frac{x}{5} + \frac{x}{7} = \frac{1}{35}$$.
a) $$\frac{1}{6}$$
b) $$\frac{1}{8}$$
c) $$\frac{1}{12}$$
d) $$\frac{1}{10}$$

Explanation: $$\frac{x}{5} + \frac{x}{7} = \frac{1}{35}$$
∴$$\frac{7*x+5*x}{5*7} = \frac{1}{35}$$
∴$$\frac{7x + 5x}{35} = \frac{1}{35}$$
∴$$\frac{12x}{35} = \frac{1}{35}$$
∴12x = 1
∴x = $$\frac{1}{12}$$.

3. Solve: 3(x – 3) = 5(x + 2).
a) $$\frac{-1}{2}$$
b) $$\frac{1}{2}$$
c) 2
d) -2

Explanation: 3(x – 3) = 5(x + 2)
∴3x – 9 = 5x + 10
∴3x – 5x = 10 – 9
∴-2x = 1
∴x = $$\frac{-1}{2}$$.

4. Solve: $$\frac{m-1}{2} + \frac{2m+3}{3}$$ = 2.
a) $$\frac{2}{3}$$
b) $$\frac{3}{2}$$
c) 3
d) 2

Explanation: $$\frac{m-1}{2} + \frac{2m+3}{3}$$ = 2
∴$$\frac{3*(m-1)}{3*2} + \frac{3*(2m+3)}{2*3}$$ = 2
∴$$\frac{3m-3+6m+9}{6}$$ = 2
∴$$\frac{9m+6}{6}$$ = 2
∴9m + 6 = 12
∴9m = 6
∴m = $$\frac{2}{3}$$.

5. Solve: 12x – 3 = 9.
a) 1
b) -1
c) 12
d) -12

Explanation: 12x – 3 = 9
∴12x = 12
∴x = 1.

6. Solve: $$\frac{2v-3}{2} + \frac{3v}{4}$$ = 12.
a) $$\frac{14}{108}$$
b) $$\frac{108}{14}$$
c) $$\frac{59}{7}$$
d) $$\frac{7}{59}$$

Explanation: $$\frac{2v-3}{2} + \frac{3v}{4}$$ = 12
∴$$\frac{4*(2v-3)}{4*2} + \frac{2*3v}{4*2}$$ = 12
∴$$\frac{8v-12+6v}{8}$$ = 12
∴8v – 12 + 6v = 12 * 8
∴14v – 12 = 96
∴14v = 108
∴v = $$\frac{108}{14} = \frac{59}{7}$$.

7. Solve: 0.25(12t – 4) = 1.
a) $$\frac{2}{3}$$
b) $$\frac{3}{2}$$
c) $$\frac{12}{11}$$
d) $$\frac{11}{12}$$

Explanation: 0.25(12t – 4) = 1
∴3t – 1 = 1
∴3t = 2
∴t = $$\frac{2}{3}$$.

8. Solve: 2y – 2 = 7y + 1.
a) $$\frac{-3}{5}$$
b) $$\frac{-5}{3}$$
c) $$\frac{2}{3}$$
d) $$\frac{3}{2}$$

Explanation: 2y – 2 = 7y + 1
∴2y – 7y = 1 + 2
∴-5y = 3
∴y = $$\frac{-3}{5}$$.

9. Solve: 3n – 13 = 13n + 31.
a) $$\frac{22}{5}$$
b) $$\frac{-22}{5}$$
c) $$\frac{-44}{10}$$
d) $$\frac{44}{10}$$

Explanation: 3n – 13 = 13n +31
∴3n – 13n = 31 + 13
∴-10n = 44
∴n = $$\frac{-44}{10} = \frac{-22}{5}$$.

10. Solve: 2x – 3 = 0.
a) $$\frac{3}{2}$$
b) $$\frac{2}{3}$$
c) $$\frac{3}{5}$$
d) $$\frac{5}{3}$$

Explanation: 2x – 3 = 0
∴2x = 3
∴x = $$\frac{3}{2}$$.

11. Solve: $$\frac{14y-12}{12y-14} = \frac{1}{2}$$
a) $$\frac{10}{16}$$
b) $$\frac{8}{5}$$
c) $$\frac{5}{8}$$
d) $$\frac{16}{10}$$

Explanation: $$\frac{14y-12}{12y-14} = \frac{1}{2}$$
∴2 * (14y – 12) = 1 * (12y – 14)
∴28y – 24 = 12y – 14
∴28y – 12y = -14 + 24
∴16y = 10
∴y = $$\frac{10}{16} = \frac{5}{8}$$.

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

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