Mathematics Multiple Choice Questions & Answers 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})
Answer: a
Clarification: (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})
Answer: c
Clarification: (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
Answer: a
Clarification: 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
Answer: a
Clarification: (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
Answer: a
Clarification: 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})
Answer: c
Clarification: (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})
Answer: a
Clarification: 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})
Answer: a
Clarification: 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})
Answer: b
Clarification: 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})
Answer: a
Clarification: 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})
Answer: c
Clarification: (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}).