ACT Math : Expressions
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Example Questions
Example Question #4 : How To Simplify Expressions
Simplify the expression:
x2 + 2x + 1
x
x + 1
2x + 1
2x
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 #992 : 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 #3 : 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 #11 : Simplifying Expressions
a # b = (a * b) + a
What is 3 # (4 # 1)?
8
27
12
20
15
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 #3 : 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 quantities are equal
The relationship cannot be determined
The mean is greater
The median is greater
The quantities are equal
If the first integer is 
This is the same as the median.
Example Question #122 : Expressions
You are told that 
Determine whether the absolute value of 
The quantities are equal
The relationship cannot be determined from the information given.
The expression is simplified as follows:
Since 
Example Question #123 : Expressions
Which best describes the relationship between 
The relationship cannot be determined from the information given.
The relationship cannot be determined from the information given.
Use substitution to determine the relationship.
For example, we could plug in 
So far it looks like the first expression is greater, but it's a good idea to try other values of x and y to be sure. This time, we'll try some negative values, say, 
This time the first quantity is smaller. Therefore the relationship cannot be determined from the information given.
Example Question #6 : Simplifying Expressions
If 
Cannot be determined
We have three variables and only two equations, so we will not be able to solve for each independent variable. We need to think of another solution.
Notice what happens if we line up the two equations and add them together.
(x + y) + (3x – y + z) = 4x + z
and 5 + 3 = 8
Lets take this equation and multiply the whole thing by 3:
3(4x + z = 8)
Thus, 12x + 3z = 24.
Example Question #1 : How To Simplify Expressions
Simplify the following expression: x3 - 4(x2 + 3) + 15
To simplify this expression, you must combine like terms. You should first use the distributive property and multiply -4 by x2 and -4 by 3.
x3 - 4x2 -12 + 15
You can then add -12 and 15, which equals 3.
You now have x3 - 4x2 + 3 and are finished. Just a reminder that x3 and 4x2 are not like terms as the x’s have different exponents.
Example Question #21 : Simplifying Expressions
Which of the following is equivalent to 
?
abc
a2/(b5c)
ab5c
b5/(ac)
ab/c
b5/(ac)
First, we can use the property of exponents that xy/xz = xy–z
Then we can use the property of exponents that states x–y = 1/xy
a–1b5c–1 = b5/ac
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