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

Card 0 of 396

Question

If , what is the value of $\frac{x^{2}+20}{x-4}$ ?

Answer

To solve this question, substitute -5 in for x in the numerator and denominator. Remember that the square of a negative number is positive.

45 / -9 = -5

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Question

If $\frac{6}{x}=\frac{9}{19}$ , then what is the value of ?

Answer

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

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Question

The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.

Answer

Let numerator = N and denominator = D.

According to the first statement,

N = (D x 5) + 4.

According to the second statement, N / 2 = 3 * D.

Let's multiply the second equation by –2 and add itthe first equation:

–N = –6D

+\[N = (D x 5) + 4\]

=

–6D + (D x 5) + 4 = 0

–1D + 4 = 0

D = 4

Thus, N = 24.

Therefore, N/D = 24/4 = 6.

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Question

$\dpi{100} \small \frac{4 }{x} = \frac{2}{25}$

Find x.

Answer

Cross multiply:

$\dpi{100} \small 4 \times 25 = 2x$

$\dpi{100} \small 100 = 2x$

$\dpi{100} \small x = 50$

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Question

Solve for .

$\frac{16}{x + 7} = \frac{2}{6}$

Answer

Cross multiply.

Dsitribute.

Solve for .

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Question

The quotient of a fraction is . If the numerator is , what is the value of the denominator?

Answer

Step 1: Set up the equation

$\frac{48x^3}{D}=12x$

Step 2: Solve for D

$\frac{48x^3}{D}=12x \rightarrow 48x^3= 12x \cdot D\rightarrow \frac{48x^3}{12x}=D$

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Question

Solve for :

$\frac{x+1}{4}-\frac{x}{3}=6$

Answer

Solve for x:

$\frac{x+1}{4}-\frac{x}{3}=6$

Step 1: Find the least common denominator, , and adjust the fractions accordingly:

$\left (\frac{3}{3} \right )\cdot \left ( \frac{x+1}{4} \right ) - \left ( \frac{4}{4} \right )\cdot \left ( \frac{x}{3} \right )=6$

$\left ( \frac{3x+3}{12} \right )-\left ( \frac{4x}{12} \right )=6$

Solve for :

$\frac{3x+3-4x}{12}=6$

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Question

For what value of is the equation $\frac{4}{12}=\frac{5}{x}$ true?

Answer

When the equation is cross multiplied, it becomes

$\ 4\cdot x=5\cdot 12 \4x = 60$ .

Hence,

$x =\frac{60}{4}$ , or .

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Question

Solve the following equation for the given variable:

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

Answer

To solve this equation we have to multiply both sides by the denominator to get rid of the fraction.

Doing this yields

Then to solve the last step is to isolate the variable by dividing both sides by 12.
Thus,

$x = \frac{2}{12}=\frac{1}{6}$ .

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Question

Solve the following equation for :

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

Reduce any fractions in your final answer.

Answer

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.
$\5x * \left(\frac{36}{5x}\right) = 4 * 5x\ ewline 36 = 20x ewline ewline \frac{36}{20} = x \ ewline \frac{9}{5}= x$

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Question

Solve for :

$\frac{3}{4}=\frac{5x+10}{20}$

Answer

To solve this problem you must cross mutiply, then set the two equations equal to each other. Your first equation is $3\left ( 20\right )$ , your second is $4\left ( 5x+10\right )=20+40$ . This gives you . Subtract from both sides, so you have , divide by on both sides and you have .

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Question

Solve for : $\frac{x}{12}=3$

Answer

To find the answer, multiply the right side by . The result is .

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Question

Solve for

$\frac{5x+1}{2} = \frac{-3x}{6}$

Answer

To solve these types of problems, you need to cross multiply the fractions

$\frac{5x+1}{2}=\frac{-3x}{6} \rightarrow (5x+1)6 = 2*-3x$ .

Then, all we need to do is distribute the , combine like terms, and solve the algebraic equation.

$30x + 6 = -6x \rightarrow 36x = -6 \rightarrow x = -\frac{1}{6}$ .

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Question

Solve for :

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

Answer

Cross multiply:

Distribute:

Solve for :

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Question

Solve for :

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

Answer

Cross-multiply:

Distribute:

Solve for x:

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Question

Solve for :

$\frac{12x+3}{2}=\frac{4}{5}$

Answer

Cross-multiply:

Distribute:

Solve for :

$x=\frac{-7}{60}$

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Question

Solve for :

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

Answer

Cross-multiply:

Solve for : $x=\frac{9}{12}$

Simplify: $x=\frac{3}{4}$

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Question

Solve for :

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

Answer

Begin by cross-multiplying:

Now, solve for .

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

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Question

Solve for :

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

Answer

Begin by cross multiplying.

Next, solve for .

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

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Question

Solve for :

$\frac{x+5}{x+4}=6$

Answer

Begin by cross multiplying:

Now, solve for :

$x=-\frac{19}{5}$

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