Question
Solve the following inequality. Click Here for help Video
−
5
(
−
2
x
+
4
)
≤
7
−5(−2x+4)≤7
x
x
−
5
(
−
2
x
+
4
)
≤
7
−5(−2x+4)≤7
x
x
Answers
Answered by
GPT-4o mini
To solve the inequality \(-5(-2x + 4) \leq 7\), we need to simplify and isolate \(x\). Here’s how we can do that step-by-step:
1. **Distribute the -5**:
\[
-5 \cdot -2x + (-5) \cdot 4 \leq 7
\]
\[
10x - 20 \leq 7
\]
2. **Add 20 to both sides**:
\[
10x - 20 + 20 \leq 7 + 20
\]
\[
10x \leq 27
\]
3. **Divide both sides by 10**:
\[
x \leq \frac{27}{10}
\]
\[
x \leq 2.7
\]
Thus, the solution to the inequality is:
\[
x \leq 2.7
\]
1. **Distribute the -5**:
\[
-5 \cdot -2x + (-5) \cdot 4 \leq 7
\]
\[
10x - 20 \leq 7
\]
2. **Add 20 to both sides**:
\[
10x - 20 + 20 \leq 7 + 20
\]
\[
10x \leq 27
\]
3. **Divide both sides by 10**:
\[
x \leq \frac{27}{10}
\]
\[
x \leq 2.7
\]
Thus, the solution to the inequality is:
\[
x \leq 2.7
\]
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