Simplify and solve the following linear equations. $3 (5 z − 7) − 2 (9 z − 11) = 4 (8 z − 13) − 17$ .

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z=8

z=3

z=2

z=5

answer is C.

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Detailed Solution

Given equation is

3 5 z − 7 − 2 9 z − 11 = 4 8 z − 13 − 17

.
Solving the bracket,

⇒ 3 5 z − 7 − 2 9 z − 11 = 4 8 z − 13 − 17 ⇒ 3 × 5 z − 3 × 7 − 2 × 9 z + 2 × 11 = 4 × 8 z − 4 × 13 − 17 ⇒ 15 z − 21 − 18 z + 22 = 32 z − 52 − 17 ⇒ − 3 z + 1 = 32 z − 69

Transposing 32z to the left-hand side and 1 to the right-hand side.

⇒ − 3 z − 32 z = − 69 − 1 ⇒ − 35 z = − 70 ⇒ z = − 70 − 35 ⇒ z = 2

Hence, the value of variable z is 2.
Correct option is 3.

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