Asked by Slim Shady
Solve the following inequality for x.
ax - 3 < 17
ax - 3 < 17
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the inequality \( ax - 3 < 17 \), follow these steps:
1. Add 3 to both sides of the inequality:
\[
ax < 17 + 3
\]
\[
ax < 20
\]
2. Now, divide both sides by \( a \). Note that the direction of the inequality will change if \( a < 0 \):
- If \( a > 0 \):
\[
x < \frac{20}{a}
\]
- If \( a < 0 \):
\[
x > \frac{20}{a}
\]
- If \( a = 0 \), the inequality \( -3 < 17 \) is always true, meaning \( x \) can be any real number.
So, the solution to the inequality depends on the value of \( a \):
- If \( a > 0 \):
\[
x < \frac{20}{a}
\]
- If \( a < 0 \):
\[
x > \frac{20}{a}
\]
- If \( a = 0 \):
\[
x \text{ is any real number.}
\]
1. Add 3 to both sides of the inequality:
\[
ax < 17 + 3
\]
\[
ax < 20
\]
2. Now, divide both sides by \( a \). Note that the direction of the inequality will change if \( a < 0 \):
- If \( a > 0 \):
\[
x < \frac{20}{a}
\]
- If \( a < 0 \):
\[
x > \frac{20}{a}
\]
- If \( a = 0 \), the inequality \( -3 < 17 \) is always true, meaning \( x \) can be any real number.
So, the solution to the inequality depends on the value of \( a \):
- If \( a > 0 \):
\[
x < \frac{20}{a}
\]
- If \( a < 0 \):
\[
x > \frac{20}{a}
\]
- If \( a = 0 \):
\[
x \text{ is any real number.}
\]
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