Question

15.
Solve the inequality.

5c – 20 ≤ 15c + 10

Answer 1

To solve the inequality \(5c - 20 \leq 15c + 10\), we can follow these steps:

1. First, we'll get all terms involving \(c\) on one side and constant terms on the other side. Start by subtracting \(15c\) from both sides:

\[
5c - 15c - 20 \leq 10
\]

This simplifies to:

\[
-10c - 20 \leq 10
\]

2. Next, add \(20\) to both sides to isolate the term with \(c\):

\[
-10c \leq 10 + 20
\]

This gives:

\[
-10c \leq 30
\]

3. Now, divide both sides by \(-10\). Remember that when dividing or multiplying both sides of an inequality by a negative number, we must reverse the inequality sign:

\[
c \geq -3
\]

Therefore, the solution to the inequality is:

\[
c \geq -3
\]

In interval notation, this can be written as:

\[
[-3, \infty)
\]