One-Step Inequalities - Pre Algebra

1. Solve $5x \ge 35$.

   $x \ge 7$. Divide both sides by 5; the symbol stays the same.

2. Solve $\frac{x}{-2} > 5$.

   $x < -10$. Multiplying by $-2$ reverses the symbol.

3. Solve $-3x \ge -15$.

   $x \le 5$. Dividing by $-3$ reverses the symbol.

4. Solve $-x \ge 6$.

   $x \le -6$. Multiplying by $-1$ reverses the symbol.

5. Pens cost 3.50 dollars each and there are 28 dollars to spend. Solving $3.5p \le 28$ gives what maximum number of pens?

   8 pens. Dividing by 3.5 gives $p \le 8$.

6. Solve $x - 3 \le -1$.

   $x \le 2$. Add 3 to both sides.

7. Solve $x + 4 > 9$.

   $x > 5$. Subtract 4 from both sides.

8. Solve $12 < x + 5$.

   $x > 7$. Subtract 5 to get $7 < x$, which is the same as $x > 7$.

9. Solve $-2x < 8$.

   $x > -4$. Dividing by $-2$ reverses the symbol.

10. Which operations on both sides of an inequality never change the direction of the symbol?

    Adding or subtracting any number, and multiplying or dividing by a positive number.

11. When must the inequality symbol be reversed while solving?

    When both sides are multiplied or divided by a negative number.

12. How is the solution $x \ge -2$ shown on a number line?

    A closed circle at $-2$ with shading to the right.

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