Two-Step Equations - Pre Algebra

1. Solve $10 - 3x = 31$.

   $x = -7$. Subtract 10 to get $-3x = 21$, then divide by $-3$.

2. Solve $\frac{x - 4}{2} = 9$.

   $x = 22$. Multiply by 2 to get $x - 4 = 18$, then add 4.

3. What does substituting $x = 3$ into $4x - 5 = 7$ show?

   $12 - 5 = 7$ is true, so $x = 3$ is the solution.

4. Solve $\frac{2}{3}x + 1 = 9$.

   $x = 12$. Subtract 1 to get $\frac{2}{3}x = 8$, then multiply by $\frac{3}{2}$.

5. In what order are operations usually undone when solving a two-step equation such as $ax + b = c$?

   Undo the addition or subtraction first, then the multiplication or division: the reverse of the order of operations.

6. Solve $0.5x - 1 = 3$.

   $x = 8$. Add 1 to get $0.5x = 4$, then divide by 0.5.

7. Solve $\frac{x}{4} + 3 = 7$.

   $x = 16$. Subtract 3, then multiply by 4.

8. Solve $2x + 5 = 17$.

   $x = 6$. Subtract 5, then divide by 2.

9. A student divides only 21 by 3 when solving $3x + 6 = 21$. What is the correct solution?

   $x = 5$. Dividing both sides by 3 must divide every term: $x + 2 = 7$.

10. Solve $-5x + 2 = -18$.

    $x = 4$. Subtract 2 to get $-5x = -20$, then divide by $-5$.

11. Solve $3x - 4 = 11$.

    $x = 5$. Add 4, then divide by 3.

12. Solve $-\frac{x}{2} - 3 = 1$.

    $x = -8$. Add 3 to get $-\frac{x}{2} = 4$, then multiply by $-2$.

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