To solve the inequality [tex]\(7x - 35 < 2(x - 5)\)[/tex], we need to follow a step-by-step process:
Step 1: Distribute the term on the right side.
[tex]\[
7x - 35 < 2(x - 5)
\][/tex]
Distribute the 2 to both terms inside the parentheses:
[tex]\[
7x - 35 < 2x - 10
\][/tex]
Step 2: Move all terms involving [tex]\(x\)[/tex] to one side of the inequality.
Subtract [tex]\(2x\)[/tex] from both sides to isolate [tex]\(x\)[/tex] on one side:
[tex]\[
7x - 2x - 35 < -10
\][/tex]
Step 3: Simplify the terms.
Combine like terms:
[tex]\[
5x - 35 < -10
\][/tex]
Step 4: Isolate the [tex]\(x\)[/tex]-term.
Add 35 to both sides of the inequality to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
5x - 35 + 35 < -10 + 35
\][/tex]
[tex]\[
5x < 25
\][/tex]
Step 5: Solve for [tex]\(x\)[/tex].
Divide both sides by 5 to isolate [tex]\(x\)[/tex]:
[tex]\[
x < 5
\][/tex]
Therefore, the solution to the inequality [tex]\(7x - 35 < 2(x - 5)\)[/tex] is:
[tex]\[
x < 5
\][/tex]
