ACT Math : Expressions
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Example Questions
Example Question #6 : How To Simplify An Expression
Which of the following expressions are equivalent to b for all non-zero real numbers a, b, x, and y such that 
None of the answers are correct
Cross multiply to get 2xb = 3ya2, then divide by 2x to get b on one side of the equal sign by itself.
Example Question #1 : Simplifying Expressions
A store in California specializes in the sale of custom t-shirts and is growing rapidly. In their second year of business, they doubled the sales from the first year, and in the third year, they sold 50,000 more t -shirts than their second year. In their fourth year, they doubled their sales from the third year. If in the fourth year of business, the store sold 300,000 shirts, how many did they sell in the second year?
150,000
250,000
25,000
50,000
100,000
100,000
This question is a bit wordy, so it is tough to not get lost in it, it usually helps to write down the pertinent information on a separate sheet of paper. In this case, you should have written that year 4 = 2 x year 3 = 300,000
so, 300,000 = 2 x year 3
divide each side by 2 and we get
150,000 sold in year 3. We are told that year 3 = year 2 +50,000
so, subtracting 50,000 from each side yields
year 3 - 50,000 = total sales from year 2
150,000 - 50,000 = total sales for year 2 = 100,000
Example Question #2 : How To Simplify An Expression
Which of the following values is the greatest?
324
164
28
49
82
324
In order to compare each quantity, we need to rewrite each one using the same base. A common base that would be easy to use would be 2, because we can write 2, 4, 8, 16, and 32 all as a power of 2. We also need to remember that when taking an exponent to an exponent, we have to multiple the two exponents together.
28 = 28
82 = (23)2 = 26
164 = (24)4 = 216
49 = (22)9 = 218
324 = (25)4 = 220
When we compare all of the numbers as powers of 2, we realize that 220 is the largest. Thus, the answer is 324.
Example Question #81 : Expressions
Which of the following expressions is equivalent to 4x2 + 10x – 6?
First, pull out a common factor of 2 to get 2(2x2 + 5x – 3). Then factor the quadratic so that the x terms add to 5x and the numbers multiply to - 3, resulting in 2(2x – 1)(x + 3).
Example Question #1 : How To Simplify An Expression
What is the value of x when 3x + 5 = 2x – 7?
12/5
5/12
–12
12
–9
–12
To answer this question we need to isolate x. A useful first step is to subtract 5 from both sides. The expression then becomes 3x = 2x – 12. Then we can subtract 2x from both sides. This leaves x = –12.
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 : Solving Linear Equations In 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:
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