Question
Solve the inequality for \( x \) \[ 23>-7+6 x \] Simplify your answer as much as possible.
Ask by Boone Griffiths. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x < 5 \)
Solution
To solve the inequality:
\[
23 > -7 + 6x
\]
we want to find all values of \( x \) that make this statement true. Here's a step-by-step solution:
1. **Add 7 to both sides** to isolate the term with \( x \) on one side:
\[
23 + 7 > 6x
\]
\[
30 > 6x
\]
2. **Divide both sides by 6** to solve for \( x \):
\[
\frac{30}{6} > x
\]
\[
5 > x
\]
3. **Rewrite the inequality** to present it in a more conventional form:
\[
x < 5
\]
**Solution:** All real numbers \( x \) such that \( x \) is less than 5.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To solve the inequality \( 23 > -7 + 6x \), we first isolate \( x \). First, add \( 7 \) to both sides: \[ 23 + 7 > 6x \] \[ 30 > 6x \] Now, divide both sides by \( 6 \) (note that since we're dividing by a positive number, the inequality direction remains unchanged): \[ \frac{30}{6} > x \] \[ 5 > x \] This can also be written as: \[ x < 5 \] So the solution to the inequality is: \[ x < 5 \]
