Question

mathematics 9
two step equations assignment
solve the following equations by isolating the variable.

• show all of your work
• for decimals: round to the nearest tenth
• for fractions: reduce to lowest terms

1. $8x + 6 = 10$
2. $1.2y + 4 = -9$
3. $-2.4m + 9 = 8$
4. $\frac{2}{3}x - 9 = -4$

1. $\frac{-5}{4}z + 3 = -1\frac{2}{3}$
2. $\frac{x}{6} + 4 = 4.5$
3. $\frac{8}{x} + 1.3 = -4.5$
4. $2n + \frac{1}{2} = \frac{3}{4}$

1. $\frac{k}{2} - \frac{3}{4} = 2\frac{3}{8}$
2. $\frac{h}{1.6} + 3.3 = 1.8$

Explanation:

1. Equation: $8x + 6 = 10$

Step1: Subtract 6 from both sides

$8x + 6 - 6 = 10 - 6$
$8x = 4$

Step2: Divide by 8 on both sides

$x = \frac{4}{8} = \frac{1}{2}$

2. Equation: $1.2y + 4 = -9$

Step1: Subtract 4 from both sides

$1.2y + 4 - 4 = -9 - 4$
$1.2y = -13$

Step2: Divide by 1.2 on both sides

$y = \frac{-13}{1.2} \approx -10.8$

3. Equation: $-2.4m + 9 = 8$

Step1: Subtract 9 from both sides

$-2.4m + 9 - 9 = 8 - 9$
$-2.4m = -1$

Step2: Divide by -2.4 on both sides

$m = \frac{-1}{-2.4} \approx 0.4$

4. Equation: $\frac{2}{3}x - 9 = -4$

Step1: Add 9 to both sides

$\frac{2}{3}x - 9 + 9 = -4 + 9$
$\frac{2}{3}x = 5$

Step2: Multiply by $\frac{3}{2}$ on both sides

$x = 5 \times \frac{3}{2} = \frac{15}{2}$

5. Equation: $\frac{-5}{4}z + 3 = -1\frac{2}{3}$

Step1: Convert mixed number, subtract 3

$-1\frac{2}{3} = -\frac{5}{3}$
$\frac{-5}{4}z + 3 - 3 = -\frac{5}{3} - 3$
$\frac{-5}{4}z = -\frac{5}{3} - \frac{9}{3} = -\frac{14}{3}$

Step2: Multiply by $\frac{-4}{5}$ on both sides

$z = -\frac{14}{3} \times \frac{-4}{5} = \frac{56}{15}$

6. Equation: $\frac{x}{6} + 4 = 4.5$

Step1: Subtract 4 from both sides

$\frac{x}{6} + 4 - 4 = 4.5 - 4$
$\frac{x}{6} = 0.5$

Step2: Multiply by 6 on both sides

$x = 0.5 \times 6 = 3$

7. Equation: $\frac{8}{x} + 1.3 = -4.5$

Step1: Subtract 1.3 from both sides

$\frac{8}{x} + 1.3 - 1.3 = -4.5 - 1.3$
$\frac{8}{x} = -5.8$

Step2: Solve for x

$x = \frac{8}{-5.8} \approx -1.4$

8. Equation: $2n + \frac{1}{2} = \frac{3}{4}$

Step1: Subtract $\frac{1}{2}$ from both sides

$2n + \frac{1}{2} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4}$
$2n = \frac{1}{4}$

Step2: Divide by 2 on both sides

$n = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$

9. Equation: $\frac{k}{2} - \frac{3}{4} = 2\frac{3}{8}$

Step1: Convert mixed number, add $\frac{3}{4}$

$2\frac{3}{8} = \frac{19}{8}$, $\frac{3}{4} = \frac{6}{8}$
$\frac{k}{2} - \frac{6}{8} + \frac{6}{8} = \frac{19}{8} + \frac{6}{8}$
$\frac{k}{2} = \frac{25}{8}$

Step2: Multiply by 2 on both sides

$k = \frac{25}{8} \times 2 = \frac{25}{4}$

10. Equation: $\frac{h}{16} + 3.3 = 1.8$

Step1: Subtract 3.3 from both sides

$\frac{h}{16} + 3.3 - 3.3 = 1.8 - 3.3$
$\frac{h}{16} = -1.5$

Step2: Multiply by 16 on both sides

$h = -1.5 \times 16 = -24$

Answer:

1. $x = \frac{1}{2}$
2. $y \approx -10.8$
3. $m \approx 0.4$
4. $x = \frac{15}{2}$
5. $z = \frac{56}{15}$
6. $x = 3$
7. $x \approx -1.4$
8. $n = \frac{1}{8}$
9. $k = \frac{25}{4}$
10. $h = -24$