Question

1. solve the equation. show your thinking.

$4(2a - 6)+7=-10 + 4a$

Explanation:

Step1: Expand the left - hand side

First, we use the distributive property \(c(a + b)=ca+cb\) to expand \(4(2a - 6)\).
\(4(2a-6)+7=4\times2a-4\times6 + 7=8a-24 + 7\)
Then simplify \(8a-24 + 7\) to get \(8a-17\). So the equation becomes \(8a-17=-10 + 4a\).

Step2: Move the terms with \(a\) to one side and constants to the other

Subtract \(4a\) from both sides of the equation:
\(8a-4a-17=-10 + 4a-4a\)
\(4a-17=-10\)
Then add 17 to both sides:
\(4a-17 + 17=-10 + 17\)
\(4a=7\)

Step3: Solve for \(a\)

Divide both sides of the equation \(4a = 7\) by 4:
\(a=\frac{7}{4}=1.75\)

Answer:

\(a=\frac{7}{4}\) (or \(a = 1.75\))