Answer :
We start with the inequality
[tex]$$-10x - 25 \leq -220.$$[/tex]
Step 1. Add 25 to both sides:
[tex]$$-10x - 25 + 25 \leq -220 + 25,$$[/tex]
[tex]$$-10x \leq -195.$$[/tex]
Step 2. Divide both sides by [tex]$-10$[/tex]. Remember, dividing by a negative number reverses the inequality sign:
[tex]$$x \geq \frac{-195}{-10}.$$[/tex]
[tex]$$x \geq 19.5.$$[/tex]
Thus, the solution for the inequality is
[tex]$$x \geq 19.5.$$[/tex]
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Next, consider the inequality
[tex]$$-10x - 25 \geq -220.$$[/tex]
Step 1. Add 25 to both sides:
[tex]$$-10x \geq -220 + 25,$$[/tex]
[tex]$$-10x \geq -195.$$[/tex]
Step 2. Divide both sides by [tex]$-10$[/tex], reversing the inequality:
[tex]$$x \leq \frac{-195}{-10}.$$[/tex]
[tex]$$x \leq 19.5.$$[/tex]
Thus, the solution for the inequality is
[tex]$$x \leq 19.5.$$[/tex]
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Now, we solve the equation
[tex]$$-3x - 12 = 60.$$[/tex]
Step 1. Add 12 to both sides:
[tex]$$-3x - 12 + 12 = 60 + 12,$$[/tex]
[tex]$$-3x = 72.$$[/tex]
Step 2. Divide both sides by [tex]$-3$[/tex]:
[tex]$$x = \frac{72}{-3},$$[/tex]
[tex]$$x = -24.$$[/tex]
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In summary:
1. For the inequality [tex]$$-10x - 25 \leq -220,$$[/tex] we found [tex]$$x \geq 19.5.$$[/tex]
2. For the inequality [tex]$$-10x - 25 \geq -220,$$[/tex] we found [tex]$$x \leq 19.5.$$[/tex]
3. For the equation [tex]$$-3x - 12 = 60,$$[/tex] we found [tex]$$x = -24.$$[/tex]
[tex]$$-10x - 25 \leq -220.$$[/tex]
Step 1. Add 25 to both sides:
[tex]$$-10x - 25 + 25 \leq -220 + 25,$$[/tex]
[tex]$$-10x \leq -195.$$[/tex]
Step 2. Divide both sides by [tex]$-10$[/tex]. Remember, dividing by a negative number reverses the inequality sign:
[tex]$$x \geq \frac{-195}{-10}.$$[/tex]
[tex]$$x \geq 19.5.$$[/tex]
Thus, the solution for the inequality is
[tex]$$x \geq 19.5.$$[/tex]
---
Next, consider the inequality
[tex]$$-10x - 25 \geq -220.$$[/tex]
Step 1. Add 25 to both sides:
[tex]$$-10x \geq -220 + 25,$$[/tex]
[tex]$$-10x \geq -195.$$[/tex]
Step 2. Divide both sides by [tex]$-10$[/tex], reversing the inequality:
[tex]$$x \leq \frac{-195}{-10}.$$[/tex]
[tex]$$x \leq 19.5.$$[/tex]
Thus, the solution for the inequality is
[tex]$$x \leq 19.5.$$[/tex]
---
Now, we solve the equation
[tex]$$-3x - 12 = 60.$$[/tex]
Step 1. Add 12 to both sides:
[tex]$$-3x - 12 + 12 = 60 + 12,$$[/tex]
[tex]$$-3x = 72.$$[/tex]
Step 2. Divide both sides by [tex]$-3$[/tex]:
[tex]$$x = \frac{72}{-3},$$[/tex]
[tex]$$x = -24.$$[/tex]
---
In summary:
1. For the inequality [tex]$$-10x - 25 \leq -220,$$[/tex] we found [tex]$$x \geq 19.5.$$[/tex]
2. For the inequality [tex]$$-10x - 25 \geq -220,$$[/tex] we found [tex]$$x \leq 19.5.$$[/tex]
3. For the equation [tex]$$-3x - 12 = 60,$$[/tex] we found [tex]$$x = -24.$$[/tex]
