To solve the inequalities \(3x - 4 < 5\) and \(3x + 4 \geq 25\), we will solve each one separately:
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For the inequality \(3x - 4 < 5\): \[ 3x - 4 < 5 \] Add 4 to both sides: \[ 3x < 9 \] Divide by 3: \[ x < 3 \]
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For the inequality \(3x + 4 \geq 25\): \[ 3x + 4 \geq 25 \] Subtract 4 from both sides: \[ 3x \geq 21 \] Divide by 3: \[ x \geq 7 \]
So, combining both results, the solution set is: \[ x < 3 \quad \text{or} \quad x \geq 7 \]
Now let’s analyze the provided options to see which one matches our solution set:
- \(-3 ≤ x < 7\) - Not correct since it doesn't include \(x \geq 7\).
- \(1 ≤ x < -7\) - Not correct since the range is invalid.
- \(x > 3 \text{ or } x ≤ 7\) - Not correct since it doesn't match our conditions.
- \(x < 3 \text{ or } x \geq 7\) - This is correct.
Therefore, the choice that best describes the solution set is: \(x < 3 \text{ or } x \geq 7\).
If this exact option is not available, please double-check the list of choices.