Question

solve the equation. what is the value of h?
there are many ways to start solving this equation. one way is to use the distributive property to rewrite the left side. this would eliminate the parentheses on the left so that we are closer to isolating h on the left. start by distributing the 6 to the h. how can you represent 6·h?
6(h -2) = 12
□ - — = 12

Explanation:

Step1: Apply Distributive Property

The distributive property states that \( a(b - c)=ab - ac \). For \( 6(h - 2) \), distribute 6 to \( h \) and -2. So \( 6\times h=6h \) and \( 6\times2 = 12 \). Thus, \( 6(h - 2)=6h-12 \).

Step2: Solve for h

Now we have the equation \( 6h-12 = 12 \). Add 12 to both sides: \( 6h-12 + 12=12 + 12 \), which simplifies to \( 6h=24 \). Then divide both sides by 6: \( \frac{6h}{6}=\frac{24}{6} \), so \( h = 4 \). But first, for the boxed part in the given step, after distributing, we get \( 6h-12=12 \). So the first box is \( 6h \) and the second blank is 12. Then solving gives \( h = 4 \).

Answer:

For the first box: \( 6h \), the second blank: \( 12 \), and the value of \( h \) is \( 4 \).