Question

How do I solve the inequality 5 - 2x ≥ 7?

Answer 1

To solve the inequality \(5 - 2x \geq 7\), follow these steps:

1. **Isolate the variable term**: Start by subtracting 5 from both sides of the inequality:

\[
5 - 2x - 5 \geq 7 - 5
\]

This simplifies to:

\[
-2x \geq 2
\]

2. **Solve for \(x\)**: Next, divide both sides by -2. Remember that when you divide or multiply both sides of an inequality by a negative number, you need to reverse the inequality symbol:

\[
x \leq \frac{2}{-2}
\]

Simplifying the right side gives:

\[
x \leq -1
\]

So the solution to the inequality \(5 - 2x \geq 7\) is:

\[
x \leq -1
\]

This means that \(x\) can take any value less than or equal to -1.