Determine the value of h that satisfies the equation below: 5 - 2(3h - 4) = 6h - 4(h + 4) … — Armed Services Vocational Aptitude Battery (ASVAB)

Determine the value of $h$ that satisfies the equation below:

5 - 2(3h - 4) = 6h - 4(h + 4) - 3

Answer: 4

The correct value is 4.

The equation is solved by first distributing the coefficients across the parentheses, which yields

5 - 6h + 8 = 6h - 4h - 16 - 3

. Combining like terms on both sides simplifies the equation to

13 - 6h = 2h - 19

. Adding

6h

and

19

to both sides isolates the variable, resulting in

32 = 8h

. Dividing by

8

gives the final answer of

4

Apply the distributive property.

5 - 6h + 8 = 6h - 4h - 16 - 3

Multiply the terms inside the parentheses by their outside coefficients, carefully distributing the negative signs.

Combine like terms on the left side.

13 - 6h = 6h - 4h - 16 - 3

Combine the constant terms

5

and

8

Combine like terms on the right side.

13 - 6h = 2h - 19

Combine the variable terms (

6h - 4h = 2h

) and the constant terms (

-16 - 3 = -19

Isolate the variable

h

13 + 19 = 2h + 6h

Add

6h

to both sides and add

19

to both sides to group the variables and constants.

Solve for the final value.

32 = 8h \rightarrow h = 4

Simplify the addition and divide by

8

to find

h

Solving One-Variable Linear Equations

Estimated Time:1m 30s

Question