Question

part d
solve the inequality for the variable x. use opposite operations on both sides of the inequality until you get x on one side of the inequality by itself.
the problem statement says there were fewer than 51 oranges left when theresa finished bagging:
number of oranges left < 51.
the inequality 213 - 3x < 51 (or -3x + 213 < 51) represents the scenario.

Explanation:

Step1: Subtract 213 from both sides

To isolate the term with \( x \), we subtract 213 from both sides of the inequality \( 213 - 3x < 51 \).

$$ 213 - 3x - 213 < 51 - 213 $$

Simplifying both sides, we get:

$$ -3x < -162 $$

Step2: Divide by -3 (and reverse inequality)

When dividing an inequality by a negative number, the direction of the inequality sign reverses. We divide both sides by -3.

$$ \frac{-3x}{-3} > \frac{-162}{-3} $$

Simplifying both sides, we get:

$$ x > 54 $$

Answer:

\( x > 54 \)