Question

Solve the inequality: (3/4) x + 10 > -1

x < 12
x > 12
x < - 12

Answer 1

To solve the inequality \((\frac{3}{4}) x + 10 > -1\), we'll start by isolating \(x\).

1. Subtract \(10\) from both sides:
\[
\frac{3}{4} x > -1 - 10
\]

2. Simplifying the right side gives:
\[
\frac{3}{4} x > -11
\]

3. Now, multiply both sides by \(\frac{4}{3}\) (remember that since \(\frac{4}{3}\) is positive, the direction of the inequality does not change):
\[
x > -11 \times \frac{4}{3}
\]

4. Calculating \(-11 \times \frac{4}{3}\):
\[
-11 \times \frac{4}{3} = -\frac{44}{3}
\]

So, we get:
\[
x > -\frac{44}{3}
\]

Now we will compare this result to the options given:

- \(x < 12\)
- \(x > 12\)
- \(x < -12\)

None of the provided options match the solution \(x > -\frac{44}{3}\) (which is approximately \(x > -14.67\)). However, it's clear that this means \(x\) is greater than a negative value, which does not match any of the inequalities listed.

Thus, the conclusion is that the provided options don't include the correct interpretation of the inequality solution.

To summarize:
The correct solution is \(x > -\frac{44}{3}\) (approximately \(x > -14.67\)).