How to solve for a variable as part of a fraction

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ACT Math › How to solve for a variable as part of a fraction

Questions 1 - 10

1

Solve the following equation for :

$\frac{36}{5x} = 4$ .

Reduce any fractions in your final answer.

$x = \frac{9}{5}$

$x = \frac{36}{20}$

$x = \frac{5}{9}$

Explanation

To solve an equation with a variable in a fraciton, treat the denominator as a constant value and multiply both sides of the equation by the denominator in order to eliminate it.
$\5x * \left(\frac{36}{5x}\right) = 4 * 5x\ ewline 36 = 20x ewline ewline \frac{36}{20} = x \ ewline \frac{9}{5}= x$

2

Solve for :

$\frac{14}{x+3}=\frac{2}{3}$

Explanation

Cross multiply:

Distribute:

Solve for :

3

Solve for :

$\frac{x+4}{3}=\frac{4}{5}$

$-\frac{8}{5}$

$-\frac{5}{8}$

$\frac{2}{3}$

$\frac{1}{3}$

Explanation

Begin by cross-multiplying:

Now, solve for .

$x=-\frac{8}{5}$

4

Solve for :

$\frac{x^{2}}{4}=\frac{18}{8}$

Explanation

Begin by cross-multiplying.

$8x^{2}=72$

$x^{2}=9$

5

Solve for .

$\frac{3}{2x}=\frac{7}{9}$

$\frac{27}{14}$

$\frac{3}{2}$

$\frac{29}{14}$

Explanation

First, cross multiply.

Now, simplify and solve for .

$x=\frac{27}{14}$

6

Solve for :

$\frac{x+3}{4}=\frac{3}{4}$

$\frac{1}{2}$

$\frac{4}{3}$

Explanation

First, cross multiply:

Now, solve for x.

7

Solve for .

$\frac{3x}{5}=\frac{13}{10}$

$\frac{13}{6}$

$\frac{7}{3}$

Explanation

First, cross multiply.

$x=\frac{65}{30}=\frac{13}{6}$

8

Solve for :

$\frac{2}{x-2}=\frac{3}{4}$

$\frac{14}{3}$

$\frac{13}{3}$

$\frac{4}{3}$

$\frac{11}{3}$

Explanation

Begin by cross multiplying.

Next, solve for .

$x=\frac{14}{3}$

9

Solve for :

$\frac{x+7}{4}=\frac{3}{2}$

$\frac{3}{2}$

$\frac{2}{3}$

Explanation

Cross-multiply:

Distribute:

Solve for x:

10

Solve for .

$\frac{x-3}{3}=\frac{12}{7}$

$\frac{57}{7}$

$\frac{58}{7}$

$\frac{40}{3}$

$\frac{49}{4}$

Explanation

First, cross-multiply.

Now, simplify and solve for .

$x=\frac{57}{7}$

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