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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