Questions: Solve the compound inequality. 4x - 5 ≤ -25 or 3x - 2 ≥ 16 Graph the solution on the number line.

Transcript text: Solve the compound inequality. \[ 4 x-5 \leq-25 \text { or } 3 x-2 \geq 16 \] Graph the solution on the number line.

Solution

Solution Steps

Step 1: Solve the first inequality

4x - 5 \leq -25

Add 5 to both sides: $4x - 5 + 5 \leq -25 + 5$ $4x \leq -20$

Divide both sides by 4: $x \leq -5$

Step 2: Solve the second inequality

3x \geq 16

Divide both sides by 3: $x \geq \frac{16}{3}$ $x \geq 5.33$

Step 3: Combine the solutions

The compound inequality is $x \leq -5$ or $x \geq \frac{16}{3}$ .

Final Answer

The solution to the compound inequality is $x \leq -5$ or $x \geq \frac{16}{3}$ .

Graphically, this can be represented on a number line with a closed circle at -5 extending to the left and a closed circle at $\frac{16}{3}$ extending to the right.

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