SAT Math : Simplifying Expressions
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Example Questions
Example Question #1 : Simplifying Expressions
If x + y = 4, what is the value of x + y – 6?
2
–2
0
6
4
–2
Substitute 4 for x + y in the expression given.
4 minus 6 equals –2.
Example Question #1 : Simplifying Expressions
If 6 less than the product of 9 and a number is equal to 48, what is the number?
4
3
6
5
6
Write an equation for the written expression: 9x – 6 = 48. When we solve for x we get x = 6.
Example Question #2 : How To Simplify An Expression
If x 
y = (5x - 4y)/y , find the value of y if 6 y = 2.
4
5
10
2
5
If we substitute 6 in for x in the given equation and set our answer to 2, we can solve for y algebraically. 30 minus 4y divided by y equals 2 -->2y =30 -4y --> 6y =30 --> y=5. We could also work from the answers and substitute each answer in and solve.
Example Question #2 : Simplifying Expressions
Evaluate: (2x + 4)(x2 – 2x + 4)
2x3 – 4x2 + 8x
4x2 + 16x + 16
2x3 + 8x2 – 16x – 16
2x3 – 8x2 + 16x + 16
2x3 + 16
2x3 + 16
Multiply each term of the first factor by each term of the second factor and then combine like terms.
(2x + 4)(x2 – 2x + 4) = 2x3 – 4x2 + 8x + 4x2 – 8x + 16 = 2x3 + 16
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
Example Question #5 : Simplifying Expressions
Solve for x: 2y/3b = 5x/7a
6ab/7y
7ab/6y
15b/14ay
14ay/15b
5by/3a
14ay/15b
Cross multiply to get 14ay = 15bx, then divide by 15b to get x by itself.
Example Question #2 : Simplifying Expressions
Three consecutive positive integers are added together. If the largest of the three numbers is m, find the sum of the three numbers in terms of m.
3m + 6
3m – 3
3m – 6
3m
3m + 3
3m – 3
Three consecutive positive integers are added together. If the largest of the three numbers is m, find the sum of the three numbers in terms of m.
If m is the largest of three consecutive positive integers, then the integers must be:
m – 2, m – 1, and m, where m > 2.
The sum of these three numbers is:
m - 2 + m – 1 + m = 3m – 3
Example Question #455 : Problem Solving
Sophie travels f miles in g hours. She must drive another 30 miles at the same rate. Find the total number of hours, in terms of f and g, that the trip will take.
g + f
g + f + 30
Using d = rt, we know that first part of the trip can be represented by f = rg. The second part of the trip can be represented by 30 = rx, where x is some unknown number of hours. Note that the rate r is in both equations because Sophie is traveling at the same rate as mentioned in the problem.
Solve each equation for the time (g in equation 1, x in equation 2).
g = f/r
x = 30/r
The total time is the sum of these two times
Note that, from equation 1, r = f/g, so
=
Example Question #8 : Simplifying Expressions
If a + b = 10 and b + c = 15, then what is the value of (c – a)/(a + 2b + c)?
150
1/5
3/2
2/3
5
1/5
Add the two equations:
a + b = 10
b + c = 15
------------
a + b + b + c = 10 + 15
a + 2b + c = 25 (this is the denominator of the answer)
Subtract the two equations:
b + c = 15
a + b = 10
------------
b + c – (a + b) = 15 – 10
c – a = 5 (this is the numerator of the answer)
5/25 = 1/5
Example Question #9 : Simplifying Expressions
If a = 2b, 3b = c, and 2c = 3d, what is the value of d/a?
3
3/2
1
2
2/3
1
Eq 1: a = 2b
Eq 2: 3b = c
Eq 3: 2c = 3d
Rewrite Eq. 3 substituting using Eq. 2.
2(3b) = 3d (because c = 3b)
6b = 3d (simplify)
2b = d (divide by 3)
Since a and d both equal 2b, a = d. Therefore, d/a = 1.
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