College

What is the solution to this inequality?

\[ 2(x-5) \leq 40 \]

A. \[ x \leq 25 \]
B. \[ x \geq 25 \]
C. \[ x \geq -25 \]
D. \[ x \leq -25 \]

Answer :

To solve the inequality [tex]\(2(x-5) \leq 40\)[/tex], you can follow these steps:

1. Distribute the 2: Start by distributing the 2 to both terms inside the parentheses.
[tex]\[
2(x-5) = 2 \times x - 2 \times 5 = 2x - 10
\][/tex]

2. Set up the inequality: Substitute back into the inequality.
[tex]\[
2x - 10 \leq 40
\][/tex]

3. Add 10 to both sides: This step will help isolate the term with [tex]\(x\)[/tex].
[tex]\[
2x - 10 + 10 \leq 40 + 10
\][/tex]
[tex]\[
2x \leq 50
\][/tex]

4. Divide both sides by 2: Solve for [tex]\(x\)[/tex] by dividing both sides by 2.
[tex]\[
\frac{2x}{2} \leq \frac{50}{2}
\][/tex]
[tex]\[
x \leq 25
\][/tex]

Therefore, the solution to the inequality [tex]\(2(x-5) \leq 40\)[/tex] is [tex]\(x \leq 25\)[/tex].