ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store varsity tutors ibooks store

Example Questions

Example Question #3 : How To Solve For A Variable As Part Of A Fraction

Solve for \displaystyle x:

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

Possible Answers:

\displaystyle x=60

\displaystyle x=-72

\displaystyle x=-69

\displaystyle x=42

\displaystyle x=26

Correct answer:

\displaystyle x=-69

Explanation:

Solve for x:

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

Step 1: Find the least common denominator, \displaystyle 12, and adjust the fractions accordingly:

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

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

Solve for \displaystyle x:

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

\displaystyle 3x+3-4x=72

\displaystyle -x=69

\displaystyle x=-69

 

Example Question #2 : How To Solve For A Variable As Part Of A Fraction

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

Possible Answers:

9/114

3/38

7/12

none of these

38/3

Correct answer:

38/3

Explanation:

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

Example Question #1221 : Algebra

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

Find x.

Possible Answers:

\dpi{100} \small \frac{25}{8}

None

\dpi{100} \small 0.25

\dpi{100} \small \frac{8}{25}

\dpi{100} \small 50

Correct answer:

\dpi{100} \small 50

Explanation:

Cross multiply:

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

\dpi{100} \small 100 = 2x

\dpi{100} \small x = 50

Example Question #2 : How To Solve For A Variable As Part Of A Fraction

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.

Possible Answers:

\displaystyle 6

\displaystyle \frac{1}{2}

\displaystyle \frac{1}{3}

\displaystyle 12

\displaystyle 18

Correct answer:

\displaystyle 6

Explanation:

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.

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Solve the following equation for the given variable:

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

Possible Answers:

\displaystyle x = \frac{3}{4}

\displaystyle x = \frac{8}{3}

\displaystyle x = \frac{1}{5}

\displaystyle x = \frac{1}{6}

\displaystyle x = \frac{3}{2}

Correct answer:

\displaystyle x = \frac{1}{6}

Explanation:

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

Doing this yields

\displaystyle 2 = 12x 

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

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

Example Question #5 : How To Solve For A Variable As Part Of A Fraction

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

Possible Answers:

\displaystyle 6

\displaystyle 14

\displaystyle 3

\displaystyle 12

\displaystyle 15

Correct answer:

\displaystyle 15

Explanation:

When the equation is cross multiplied, it becomes

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

Hence,

\displaystyle x =\frac{60}{4}, or \displaystyle x=15

Example Question #4 : How To Solve For A Variable As Part Of A Fraction

Solve the following equation for \displaystyle x:


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

Reduce any fractions in your final answer.

Possible Answers:

\displaystyle x = 5

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

\displaystyle x = 3

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

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

Correct answer:

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

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.

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Solve for \displaystyle x\displaystyle \frac{x}{12}=3

Possible Answers:

\displaystyle 36

\displaystyle \frac{1}{36}

\displaystyle 24

\displaystyle 4

\displaystyle \frac{1}{3}

Correct answer:

\displaystyle 36

Explanation:

To find the answer, multiply the right side by \displaystyle 12. The result is \displaystyle 36=x.

Example Question #61 : Algebraic Fractions

Solve for \displaystyle x:

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

Possible Answers:

\displaystyle 1

\displaystyle 4

\displaystyle 5

\displaystyle 2

\displaystyle 3

Correct answer:

\displaystyle 1

Explanation:

To solve this problem you must cross mutiply, then set the two equations equal to each other. Your first equation is\displaystyle 3\left ( 20\right ), your second is \displaystyle 4\left ( 5x+10\right )=20+40. This gives you \displaystyle 60=20x+40. Subtract \displaystyle 40 from both sides, so you have \displaystyle 20=20x, divide by \displaystyle 20 on both sides and you have \displaystyle x=1.

Example Question #11 : How To Solve For A Variable As Part Of A Fraction

Solve for \displaystyle x:

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

Possible Answers:

\displaystyle 19.5

\displaystyle 18

\displaystyle 20

\displaystyle 16

Correct answer:

\displaystyle 18

Explanation:

Cross multiply: \displaystyle 42=2(x+3)

Distribute: \displaystyle 42=2x+6

Solve for \displaystyle x\displaystyle 36=2x

\displaystyle 18=x

Learning Tools by Varsity Tutors