ACT Math : Simplifying Expressions
Study concepts, example questions & explanations for ACT Math
All ACT Math Resources
Example Questions
Example Question #1 : How To Simplify Expressions
Simplify the following expression:
First distribute the 2:
Combine the like terms:
Example Question #991 : Algebra
There are 
Example Question #1 : Word Problems
Erin is making thirty shirts for her upcoming family reunion. At the reunion she is selling each shirt for $18 apiece. If each shirt cost her $10 apiece to make, how much profit does she make if she only sells 25 shirts at the reunion?
This problem involves two seperate multiplication problems. Erin will make $450 at the reunion but supplies cost her $300 to make the shirts. So her profit is $150.
Example Question #81 : Expressions
Which of the following is equivalent to (x)(x)(x)(x)(x–2)?
x2
x–2
x–8
x3
x2
When multiplying powers of x, we add the exponents. The first four terms are equivalent to x4.
Example Question #81 : Expressions
What is 
Reduce by first dividing all terms by 2:
Next divide the terms in the numerator by the two variables in the denominator. Remember that dividing variables with exponents is really just subtraction of those exponents:
Example Question #1 : How To Simplify Expressions
Simplify the expression:
x2 + 2x + 1
x
2x
x + 1
2x + 1
x + 1
Factor out a (2x) from the denominator, which cancels with (2x) from the numerator. Then factor the numerator, which becomes (x + 1)(x + 1), of which one of them cancels and you're left with (x + 1).
Example Question #994 : Algebra
Find 
None of the other answers
Create two equations to eliminate the absolute value function, one where the value inside the absolute value bars is assumed to be positive and another where it is assumed to be negative: 7x – 4 + 5 > –1 and -7x + 4 + 5 > –1.
The solutions for the equations, respectively, are x > -2/7 and x < -10/7. (Remember to flip the inequality sign when multiplying or dividing by a negative number.)
Example Question #1 : How To Do Distance Problems
Trevor took a road trip in his new VW Beetle. His car averages 32 miles per gallon. Gas costs $4.19 per gallon on average for the whole trip. How much would it coust to drive 3,152 miles?
To find this answer just do total miles divided by miles per gallon in order to find how many gallons of gas it will take to get from point A to Point B. Then multiply that answer by the cost of gasoline per gallon to find total amount spent on gasoline.
Example Question #991 : Algebra
a # b = (a * b) + a
What is 3 # (4 # 1)?
8
27
15
12
20
27
Work from the "inside" outward. Therefore, first solve 4 # 1 by replacing a with 4 and b with 1:
4 # 1 = (4 * 1) + 4 = 4 + 4 = 8
That means: 3 # (4 # 1) = 3 # 8. Solve this now:
3 # 8 = (3 * 8) + 3 = 24 + 3 = 27
Example Question #1 : How To Simplify An Expression
Which is the greater quantity: the median of 5 positive sequential integers or the mean of 5 positive sequential integers?
The relationship cannot be determined
The median is greater
The quantities are equal
The mean is greater
The quantities are equal
If the first integer is 
This is the same as the median.
All ACT Math Resources
