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) \(\frac{-9}{91}\)
View Answer

Answer: b
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 = \(\frac{27}{273} = \frac{9}{91}\).
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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
View Answer

Answer: a
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) \(\frac{14}{6}\)
View Answer

Answer: b
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
View Answer

Answer: a
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
View Answer

Answer: c
Explanation: 12x-13=2x*(11-12)
∴ 12x-13=22x-24x
∴ 12x-13= -2x
∴ 14x=13
∴ x=\(\frac{13}{14}\).
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6. Simplify: \(\frac{13x-1}{12}\)=12.
a) x=\(\frac{13}{145}\)
b) 13x+145=0
c) 13x=145
d) 145x+13=0
View Answer

Answer: c
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
View Answer

Answer: b
Explanation: t – 12 = 12t – 1.
∴ -11t=11
∴ t=1.
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8. Solve: 13x-2=21x+2.
a) 2x+1=0
b) 2x-1= 0
c) 1 + 2x = 0
d) 1 – 2x = 0
View Answer

Answer: a
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) \(\frac{-1}{12}\)
View Answer

Answer: a
Explanation: 3j+2=1-3j
∴ 3j+3j=1-2
∴ 6j=-1
∴ j=\(\frac{-1}{6}\).
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10. Solve: 12x+2=13x-1.
a) 1
b) 2
c) 3
d) 4
View Answer

Answer: c
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.

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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