Question

there are many ways you could solve this equation. one way you can start is by rewriting this equation without a fraction. what move can you make to get rid of the fraction on the left while keeping the equation balanced?\\
\\(\frac{3}{2}(5 + 2h)\\) = \\(2 + 2h\\)\\
options: multiply both sides of the equation by 2; divide both sides of the equation by 2; multiply both sides of the equation by 3

Explanation:

Step1: Eliminate fraction, multiply by 2

Multiply both sides by 2 to cancel the denominator:
$$2 \times \frac{3}{2}(5 + 2h) = 2 \times (2 + 2h)$$
Simplify to get:
$$3(5 + 2h) = 4 + 4h$$

Step2: Expand left-hand side

Distribute the 3 across the parentheses:
$$15 + 6h = 4 + 4h$$

Step3: Isolate h terms, subtract 4h

Subtract $4h$ from both sides:
$$15 + 6h - 4h = 4 + 4h - 4h$$
Simplify to get:
$$15 + 2h = 4$$

Step4: Isolate constant terms, subtract 15

Subtract 15 from both sides:
$$15 + 2h - 15 = 4 - 15$$
Simplify to get:
$$2h = -11$$

Step5: Solve for h, divide by 2

Divide both sides by 2:
$$h = \frac{-11}{2}$$

Answer:

$h = -\frac{11}{2}$ (or $h = -5.5$)

Additionally, the valid first step to eliminate the fraction is: Multiply both sides of the equation by 2