Question

solve the equation below, where there are h terms on both sides of the equation. what’s the value of h? add 3h to both sides, then rewrite the equation to represent the remaining values. 12 - 3h = 5 + 11h + 3h + 3h

Explanation:

Step1: Simplify left side

Add \(3h\) to \(12 - 3h\): \(12 - 3h + 3h = 12\) (the \(-3h\) and \(+3h\) cancel).

Step2: Simplify right side

Add \(3h\) to \(5 + 11h\): \(5 + 11h + 3h = 5 + 14h\) (combine like terms \(11h + 3h = 14h\)).
Now, the equation after adding \(3h\) to both sides is \(12 = 5 + 14h\).

Step3: Solve for h

Subtract 5 from both sides: \(12 - 5 = 14h\) → \(7 = 14h\).
Divide both sides by 14: \(h = \frac{7}{14} = \frac{1}{2}\).

Answer:

First, after adding \(3h\) to both sides, the equation is \(12 = 5 + 14h\). Then solving for \(h\), we get \(h = \frac{1}{2}\). The filled boxes after adding \(3h\) are \(12\) (left) and \(5 + 14h\) (right), and the value of \(h\) is \(\frac{1}{2}\).