**Solve for \[x\].**

\[12x+7< -11 \quad \maroonC{\text{ AND}} \quad 5x-8\geq40\]

Choose 1 answer:

Choose 1 answer:

Let's solve each inequality separately and find the solution set for \(x\).

### First inequality:
\[
12x + 7 < -11
\]
Subtract 7 from both sides:
\[
12x < -11 - 7
\]
\[
12x < -18
\]
Now, divide both sides by 12:
\[
x < \frac{-18}{12}
\]
\[
x < -1.5
\]

### Second inequality:
\[
5x - 8 \geq 40
\]
Add 8 to both sides:
\[
5x \geq 40 + 8
\]
\[
5x \geq 48
\]
Now, divide both sides by 5:
\[
x \geq \frac{48}{5}
\]
\[
x \geq 9.6
\]

### Combining the two results:
- From the first inequality, \(x < -1.5\).
- From the second inequality, \(x \geq 9.6\).

Since both inequalities need to be satisfied, and there is no overlap between \(x < -1.5\) and \(x \geq 9.6\), **there is no solution**.

### Final Answer:
**No solution.**

Do you want details or have any questions?

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Here are 5 related questions for practice:
1. Solve \(3x + 4 \leq -2 \quad \text{AND} \quad x + 6 > 8\).
2. Solve \(7x + 5 < 2x - 9 \quad \text{AND} \quad 6x \geq 3x + 12\).
3. Solve \(2(x - 3) > 4 \quad \text{AND} \quad x + 7 \leq 10\).
4. Find the solution set for \(4x + 1 > 3x + 4 \quad \text{AND} \quad 2x - 3 < x + 5\).
5. Solve for \(x\): \(5x - 9 \leq 2x + 3 \quad \text{AND} \quad x + 8 > 12\).

**Tip:** Always remember to combine solution sets carefully for inequalities using "AND" or "OR."

Solve for x: 12x + 7 < -11 AND 5x - 8 ≥ 40

Learn how to solve the system of inequalities 12x + 7 < -11 AND 5x - 8 ≥ 40. This problem walks through solving two separate linear inequalities, combining solution sets, and understanding why there is no solution. Suitable for students in Grades 8-10.

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