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].
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].
