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."