Question

m4|l6 strategic solving solve the equation below. whats the value of h? keep going. youre trying to get h alone on one side of the equation, and a constant alone on the other side of the equation. we can start by making sure that all the h terms are only on one side of the equation, while keeping the equation balanced? what move can you make to get rid of the 4h on the right side of the equation, while keeping the equation balanced? \\(\frac{3}{2}(5 + 2h) = 2 + 2h\\) \\(2 \cdot \frac{3}{2}(5 + 2h) = 2 \cdot (2 + 2h)\\) \\(3(5 + 2h) = 4 + 4h\\) \\(15 + 6h = 4 + 4h\\) \\(15 + 6h = 4 + 4h\\) add 4h to both sides divide both sides by 4h multiply both sides by 4h subtract 4h from both sides

Explanation:

Step1: Identify target term to eliminate

We need to remove $4h$ from the right side to gather all $h$-terms on the left.

Step2: Choose balanced operation

To keep the equation balanced, we perform the same operation on both sides. Subtracting $4h$ from both sides will eliminate $4h$ on the right.
<Expression>
$15 + 6h - 4h = 4 + 4h - 4h$
</Expression>

Step3: Simplify to isolate h terms

Combine like terms on both sides.
<Expression>
$15 + 2h = 4$
</Expression>

Step4: Isolate the h term

Subtract 15 from both sides.
<Expression>
$2h = 4 - 15$
$2h = -11$
</Expression>

Step5: Solve for h

Divide both sides by 2.
<Expression>
$h = \frac{-11}{2} = -5.5$
</Expression>

Answer:

First move: Subtract 4h from both sides
Final value of $h$: $\boldsymbol{-\frac{11}{2}}$ (or $\boldsymbol{-5.5}$)