To solve the inequality [tex]\( m - 2(m - 4) \leq 3m \)[/tex], follow these steps:
1. Expand and simplify the left-hand side: Distribute the [tex]\(-2\)[/tex] inside the parentheses:
[tex]\[
m - 2(m - 4) = m - 2m + 8
\][/tex]
Simplify the expression:
[tex]\[
m - 2m + 8 = -m + 8
\][/tex]
2. Write the inequality: Substitute the simplified expression back into the inequality:
[tex]\[
-m + 8 \leq 3m
\][/tex]
3. Isolate the variable [tex]\(m\)[/tex]: To do this, add [tex]\(m\)[/tex] to both sides of the inequality in order to get all [tex]\(m\)[/tex] terms on one side:
[tex]\[
-m + m + 8 \leq 3m + m
\][/tex]
Simplify:
[tex]\[
8 \leq 4m
\][/tex]
4. Solve for [tex]\(m\)[/tex]: Divide both sides of the inequality by 4 to isolate [tex]\(m\)[/tex]:
[tex]\[
\frac{8}{4} \leq \frac{4m}{4}
\][/tex]
Simplify:
[tex]\[
2 \leq m
\][/tex]
This can be rewritten as:
[tex]\[
m \geq 2
\][/tex]
So, the solution to the inequality [tex]\( m - 2(m - 4) \leq 3m \)[/tex] is:
[tex]\[
m \geq 2
\][/tex]
