What is the solution to the equation 9(w - 4) - 7w = 5(3w - 2)?

Solution:

Given, the equation is 9(w - 4) - 7w = 5(3w - 2)

We have to find the solution to the equation.

By multiplicative property,

9(w - 4) = 9w - 36

So, 9(w - 4) - 7w = 9w - 36 - 7w

= 2w - 36

5(3w - 2) becomes 15w - 10

So, 9(w - 4) - 7w = 5(3w - 2) becomes 2w - 36 = 15w - 10

By grouping,

-36 + 10 = 15w - 2w

-26 = 13w

w = -26/13

w = -2

Verification:

LHS: 9(w - 4) - 7w

= 9(-2 - 4) - 7(-2)

= 9(-6) - (-14)

= -54 + 14

= -40

RHS: 5(3w - 2)

= 5(3(-2) - 2)

= 5(-6 - 2)

= 5(-8)

= -40

LHS = RHS

Therefore, the solution to the given equation is w = -2.

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What is the solution to the equation 9(w - 4) - 7w = 5(3w - 2)?

Summary:

The solution to the equation 9(w - 4) - 7w = 5(3w - 2) is w = -2.