Solve the following linear equation for the variable w: 7 - 3(2w - 4) = w + 5 What is the … — Armed Services Vocational Aptitude Battery (ASVAB)

Solve the following linear equation for the variable $w$ :

7 - 3(2w - 4) = w + 5

What is the value of $w$ ?

Cevap:The value of

w

is 【2】.

The equation is solved by correctly applying the distributive property to get

7 - 6w + 12 = w + 5

, combining like terms to get

19 - 6w = w + 5

, and then using inverse operations to isolate

w

, which yields

w = 2

Distribute the -3 across the terms inside the parentheses.

7 - 6w + 12 = w + 5

The distributive property is required to expand the expression

-3(2w - 4)

before combining like terms. Remember that multiplying a negative by a negative results in a positive.

Combine the constant terms on the left side of the equation.

19 - 6w = w + 5

Adding

7

and

12

simplifies the left side.

Add

6w

to both sides of the equation.

19 = 7w + 5

This step groups all terms containing the variable

w

onto the right side.

Subtract 5 from both sides.

14 = 7w

This isolates the variable term

7w

on one side of the equation.

Divide both sides by 7.

w = 2

Dividing by the coefficient of

w

solves for the final value.

Solving linear equations involving the distributive property with negative coefficients and variables on both sides.

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