Linear Equations in One Variable Test

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Linear Equations in One Variable Test - 1

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Weekly Quiz Competition

Question 1
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Which equation correctly represents the statement, ‘Twice the sum of x and 3 is less than 24 by 8’?

A
2(x + 3) − 8 = 24

B
28 − 2x + 3 = 24

C
24 − 2(x + 3) = 8

D
24 − (2x + 3) = 8

Solution

Sum of x and 3 = x + 3

∴ Twice the sum of x and 3 = 2 (x + 3)

According to the given information:

24 − 2 (x + 3) = 8

Thus, the required equation is 24 − 2 (x + 3) = 8
Question 2
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Use the following information to answer the next question.

Shyam and Ghanshyam's house lie on either side of Ram's house on the same side of a straight road. The distance between Shyam’s and Ram’s houses is 1 km less than thrice the distance between Ram’s and Ghanshyam’s houses. The distance between Shyam’s house and Ghanshyam’s house is 7 km.

If the distance between Ram and Ghanshyam’s houses is x km, then which equation represents the given situation?

A
4x – 1 = 7

B
3x – 1 = 7

C
x – 4 = 7

D
4 – x = 7

Solution

Distance between Ram’s and Ghanshyam’s houses = x km

It is given that the distance between Shyam’s and Ram’s houses is 1 km less than thrice the distance between Ram’s and Ghanshyam’s houses.

∴ Distance between Shyam’s and Ram’s houses is 1 km less than thrice of x.

∴ Distance between Shyam’s and Ram’s houses = (3x – 1) km

Distance between Shyam’s house and Ghanshyam’s house = 7 km

∴(3x – 1) + x = 7

⇒ 4x – 1 = 7

Thus, the equation 4x – 1 = 7 represents the given situation.
Question 3
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Use the following information to answer the next question.

Ramesh bought twenty five candies for his sons Sonu, Ashu and Vicky. Sonu ate four candies more than Vicky, whereas Ashu ate seven candies less than twice the number of candies eaten by Vicky.

If Vicky ate x candies, then which equation represents the given situation?

A
3 – 4x = 25

B
4 – 3x = 25

C
4x – 3 = 25

D
3x – 4 = 25

Solution

Number of candies eaten by Vicky = x

Sonu ate 4 candies more than Vicky.

Therefore, number of candies eaten by Sonu = x + 4

Ashu ate 7 candies less than twice the number of candies eaten by Vicky.

Therefore, number of candies eaten by Ashu is 7 less than twice of x.

∴ Number of candies eaten by Ashu = 2x – 7

Total number of candies bought = 25

∴x + (x + 4) + (2x – 7) = 25

⇒ (x + x + 2x) + (4 – 7) = 25

⇒ 4x – 3 = 25

Thus, the equation 4x – 3 = 25 represents the given situation.