ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #121 : Equations / Inequalities

When , by how much does the value of  exceed the value of ?

Possible Answers:

Correct answer:

Explanation:

You must plug in  for  and  for , this means     and 

 

 

Example Question #122 : How To Find The Solution To An Equation

What is the value of  when ?

Possible Answers:

Correct answer:

Explanation:

The first step is to subtract  from both sides so you're left with . Next, you add  to both sides, giving you . The final step is to divide by , giving you .

Example Question #123 : How To Find The Solution To An Equation

Karen has  more than  times as many dollars as Susan. Karen also has  as many dollars as John would if he had  more dollars. How many dollars does Susan have, relative to John?

Possible Answers:

Correct answer:

Explanation:

First, set up our two equations. If Karen has seven dollars more than three times as many dollars as Susan, then . If Karen has half as many dollars as John would if he had two more dollars, then . The Substitution Property of Equality thus says that . Now, we simply solve for  in terms of .

Example Question #121 : How To Find The Solution To An Equation

If the third day of the year is a Wednesday, what is the 165th day?

Possible Answers:

Friday

Thursday

Tuesday

Wednesday

Monday

Correct answer:

Thursday

Explanation:

If the third day is a Wednesday, then the first day is a Monday. 23 weeks will complete a cycle with the 161st day. Therefore, the fourth day past that, 165, is a Thursday.

 

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

John, Jill, and Jack are splitting a pizza. John eats  of the pizza and Jill eats  of the pizza. How much of the pizza is left for Jack?

Possible Answers:

Correct answer:

Explanation:

We can write an equation for the amount of pizza eaten, with  as the amount left for Jack.

To solve this equation, we must find the lowest common denominator of  and . We can list the multiples of  and  to find the least common multiple:

We can see that the least common multiple of  and  is , so we can rewrite each of the fractions with a denominator of .

When we put these fractions back into the equation, we can solve for :

Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

What is the slope of a line represented by the equation:

Possible Answers:

Correct answer:

Explanation:

To solve problems where you need to find the slope of a line in a given equation, change the equation so that it matches y-intercept form:

For this equation, first move the 3x over to the other side of the equation.

            

The equation should now look like this:

Then, divide by 15 to isolate the variable .

Then simplify

Whatever number is before the x in the equation (m) is your slope.

Example Question #401 : Algebra

 Rational_5

Possible Answers:

1

2

0

–2

–1

Correct answer:

2

Explanation:

Rational_2

Rational_3

Rational_4

Example Question #402 : Algebra

Linesmb1

Possible Answers:

b/(m– 1)

–bm/(m+ 1)

b/(m+ 1)

bm/(m+ 1)

–b/(+ 1)

Correct answer:

b/(m+ 1)

Explanation:

Linesmb5

Linesmb4

Example Question #401 : Algebra

In the equation below, , , and are non-zero numbers. What is the value of in terms of and ?

Possible Answers:

Correct answer:

Explanation:

Pkm_7-21-13

Pkm2_7-21-13

Example Question #1901 : Act Math

Given the following system, find the solution:

x = y – 2

2x – 2y = 2

Possible Answers:

(1, 2)

(0, 1)

no solution

(1, 1)

(0, 0)

Correct answer:

no solution

Explanation:

When 2 equations in a system have the same slopes, they will either have no solution or infinite solutions. Since the y-intercepts are not the same, there is no solution to this system.

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