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 = \(\frac{167}{14}\)
View Answer

Answer: a
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 = \(\frac{147}{16}\).
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2. Solve: \(\frac{x}{5} + \frac{x}{7} = \frac{1}{35}\).
a) \(\frac{1}{6}\)
b) \(\frac{1}{8}\)
c) \(\frac{1}{12}\)
d) \(\frac{1}{10}\)
View Answer

Answer: c
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
View Answer

Answer: a
Explanation: 3(x – 3) = 5(x + 2)
∴3x – 9 = 5x + 10
∴3x – 5x = 10 – 9
∴-2x = 1
∴x = \(\frac{-1}{2}\).
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4. Solve: \(\frac{m-1}{2} + \frac{2m+3}{3}\) = 2.
a) \(\frac{2}{3}\)
b) \(\frac{3}{2}\)
c) 3
d) 2
View Answer

Answer: a
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
View Answer

Answer: a
Explanation: 12x – 3 = 9
∴12x = 12
∴x = 1.
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6. Solve: \(\frac{2v-3}{2} + \frac{3v}{4}\) = 12.
a) \(\frac{14}{108}\)
b) \(\frac{108}{14}\)
c) \(\frac{59}{7}\)
d) \(\frac{7}{59}\)
View Answer

Answer: c
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) \(\frac{11}{12}\)
View Answer

Answer: a
Explanation: 0.25(12t – 4) = 1
∴3t – 1 = 1
∴3t = 2
∴t = \(\frac{2}{3}\).
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8. Solve: 2y – 2 = 7y + 1.
a) \(\frac{-3}{5}\)
b) \(\frac{-5}{3}\)
c) \(\frac{2}{3}\)
d) \(\frac{3}{2}\)
View Answer

Answer: a
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) \(\frac{44}{10}\)
View Answer

Answer: b
Explanation: 3n – 13 = 13n +31
∴3n – 13n = 31 + 13
∴-10n = 44
∴n = \(\frac{-44}{10} = \frac{-22}{5}\).
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10. Solve: 2x – 3 = 0.
a) \(\frac{3}{2}\)
b) \(\frac{2}{3}\)
c) \(\frac{3}{5}\)
d) \(\frac{5}{3}\)
View Answer

Answer: a
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) \(\frac{16}{10}\)
View Answer

Answer: c
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.

To practice all areas of Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter