Solve the given inequality. Write the solution set using interval notation, then graph it.

Question

Solve the given inequality. Write the solution set using interval notation, then graph it. $$ \frac{5-5 x}{3} \geq-2 $$

UpStudy AI · Accepted Answer

To solve the inequality:

$$
\frac{5 - 5x}{3} \geq -2
$$

**Step 1: Eliminate the Fraction**

Multiply both sides of the inequality by 3 (since 3 is positive, the direction of the inequality remains unchanged):

$$
5 - 5x \geq -6
$$

**Step 2: Isolate the Variable Term**

Subtract 5 from both sides:

$$
-5x \geq -11
$$

**Step 3: Solve for $$ x $$**

Divide both sides by -5. **Remember**: Dividing by a negative number reverses the inequality sign.

$$
x \leq \frac{11}{5}
$$

$$
x \leq 2.2
$$

**Solution Set in Interval Notation:**

$$
(-\infty, \ 2.2]
$$

**Graph of the Solution:**

Below is a number line representing the solution $$ x \leq 2.2 $$.

```
<========●================>
        2.2
```

- The closed circle (●) at 2.2 indicates that 2.2 is included in the solution.
- The arrow pointing to the left (towards $$-\infty$$) shows that all numbers less than or equal to 2.2 are part of the solution.
The solution to the inequality $$ \frac{5 - 5x}{3} \geq -2 $$ is $$ x \leq 2.2 $$. In interval notation, this is written as $$ (-\infty, \ 2.2] $$.

Solve the given inequality. Write the solution set using interval notation, then graph it.

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