Question

mathematics 9
one - 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. $8x = 10$
2. $1.2x = -9$
3. $-2.4x = 8$

1. $\frac{x}{6}=4.5$
2. $\frac{x}{-12}=7$
3. $\frac{x}{4.5}=1\frac{2}{3}$

1. $\frac{-5.6}{x}=6.3$
2. $\frac{7}{x}=3\frac{1}{2}$
3. $\frac{8}{x}=-4\frac{1}{2}$

1. walmart is selling mitts for 30% off regular price. if the sale price is $34.99, what is the regular price?

Explanation:

Step1: Isolate x by dividing by 8

$x = \frac{10}{8} = \frac{5}{4}$

Step2: Isolate x by dividing by 1.2

$x = \frac{-9}{1.2} = -7.5$

Step3: Isolate x by dividing by -2.4

$x = \frac{8}{-2.4} \approx -3.3$

Step4: Isolate x by multiplying by 6

$x = 4.5 \times 6 = 27$

Step5: Isolate x by multiplying by -1.2

$x = 7 \times (-1.2) = -8.4$

Step6: Convert mixed number, multiply by 4.5

$1\frac{2}{3} = \frac{5}{3}$, so $x = \frac{5}{3} \times 4.5 = 7.5$

Step7: Rearrange to solve for x

$x = \frac{-5.6}{6.3} = -\frac{8}{9}$

Step8: Convert mixed number, rearrange for x

$3\frac{1}{2} = \frac{7}{2}$, so $x = \frac{7}{\frac{7}{2}} = 2$

Step9: Convert mixed number, rearrange for x

$-4\frac{1}{2} = -\frac{9}{2}$, so $x = \frac{8}{-\frac{9}{2}} = -\frac{16}{9}$

Step10: Set up equation for sale price

Let $p$ = regular price. Sale price = $p - 0.3p = 0.7p$. Solve $0.7p = 34.99$
$p = \frac{34.99}{0.7} \approx 49.99$

Answer:

1. $x = \frac{5}{4}$
2. $x = -7.5$
3. $x \approx -3.3$
4. $x = 27$
5. $x = -8.4$
6. $x = 7.5$
7. $x = -\frac{8}{9}$
8. $x = 2$
9. $x = -\frac{16}{9}$
10. The regular price is $\$49.99$