To solve the inequality [tex]\(4x + 6 \leq 18\)[/tex], follow these detailed steps:
1. Start with the given inequality:
[tex]\[
4x + 6 \leq 18
\][/tex]
2. Isolate the term involving [tex]\(x\)[/tex]:
- Subtract 6 from both sides of the inequality to get rid of the constant term on the left side.
[tex]\[
4x + 6 - 6 \leq 18 - 6
\][/tex]
Simplifying this, we have:
[tex]\[
4x \leq 12
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
- Divide both sides of the inequality by 4 (the coefficient of [tex]\(x\)[/tex]) to isolate [tex]\(x\)[/tex].
[tex]\[
\frac{4x}{4} \leq \frac{12}{4}
\][/tex]
Simplifying this, we get:
[tex]\[
x \leq 3
\][/tex]
Thus, the solution to the inequality [tex]\(4x + 6 \leq 18\)[/tex] is:
[tex]\[
x \leq 3
\][/tex]
