One-Step Equations - Pre Algebra

1. What inverse operation undoes multiplication by 6?

   Division by 6.

2. Solve $12 = x + 20$.

   $x = -8$. Subtract 20 from both sides.

3. What substitution confirms that $x = -5$ solves $x + 8 = 3$?

   $-5 + 8 = 3$, which is true, so $x = -5$ is the solution.

4. Solve $x - 9 = -4$.

   $x = 5$. Add 9 to both sides.

5. Solve $\frac{x}{3} = -6$.

   $x = -18$. Multiply both sides by 3.

6. Solve $x + 7 = 15$.

   $x = 8$. Subtract 7 from both sides.

7. Solve $-6x = 42$.

   $x = -7$. Divide both sides by $-6$.

8. What single step solves $y - 3.5 = 6$, and what is $y$?

   Add 3.5 to both sides; $y = 9.5$.

9. Solve $0.4x = 2.8$.

   $x = 7$. Divide both sides by 0.4.

10. Solve $-x = 9$.

    $x = -9$. Multiply or divide both sides by $-1$.

11. Why must the same operation be applied to both sides of an equation?

    To keep the equation balanced, so the two sides stay equal and the solution does not change.

12. Solve $\frac{2}{3}x = 10$.

    $x = 15$. Multiply both sides by the reciprocal $\frac{3}{2}$.

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