Question

Solve the following inequalities for the variable,
x
x.

​
5
x
+
3
≥
x
−
9
5x+3≥x−9



Solve the following inequalities for the variable,
x
x.

​
5
x
+
3
≥
x
−
9
5x+3≥x−9

Answer 1

To solve the inequality \( 5x + 3 \geq x - 9 \), we'll start by isolating \( x \).

1. **Subtract \( x \) from both sides**:
\[
5x + 3 - x \geq -9
\]
This simplifies to:
\[
4x + 3 \geq -9
\]

2. **Subtract 3 from both sides**:
\[
4x + 3 - 3 \geq -9 - 3
\]
This simplifies to:
\[
4x \geq -12
\]

3. **Divide both sides by 4**:
\[
x \geq -3
\]

Thus, the solution to the inequality \( 5x + 3 \geq x - 9 \) is:
\[
\boxed{x \geq -3}
\]