Equivalent Expressions
What is an equivalent expression:
3(x+2)
3x+6
Find the solution to the inequality :
4x<8
x<2
Write an equation for this situation:
A family of 4 drove to a concert. They paid $8 for parking, and all of their tickets were the same price. They paid $92 in total.
4x+8 = 92
x + 2 = 10
x = 8
Graph the solution to the following inequality : x<3
-
Write an equivalent expression:
2(x+5)
2x+10
Find the solution to the inequality :
3x + 2 > 11
x>3
Malaiki walked a neighbor’s dog 3 times this month and earned the same amount each time. They gave him an extra $12 at the end of the month. He earned $124 in total.
3x + 12 = 124
3x + 5 = 10
x = 5/3
Write an equation to find the width of a rectangle, that has a length of 10, and a perimeter of 100.
10 + 10 + w + w = 100
2(10+w) = 100
Write an equivalent expression :
-3(x+5)
-3x-15
Find the solution to the inequality :
-3x < 9
x > -3
Tamara baked 3 batches of cookies, each with the same amount of sugar, plus 7 extra
teaspoons for icing. She used 500 teaspoons total.
3x+7=500
5(x+4) = -25
x = -9
Factor the following :
18xy - 12y
6y(3x - 2)
Write an equivalent expression :
-7(x-5)
-7x+35
-6(x+12) < -36
x > -6
Ruth bought 10 boxes of cereal, each cost the same. The store gave her 5 extra boxes for $2 each. The total price was $38.
10x + 10 = 38
10x +5(2) = 38
Jasiah said the solution to the equation 1/2(x+12)=5 is
x = 2
Here is his work :
1/2x+6 = 5
-6 -6
1/2x = -1
/(1/2) /(1/2)
x = 2
What was his error?
A negative divided by a positive is a negative.
Graph the solution to the following inequality :
-4y + 2 less than or equal to 18
y is greater than or equal to -4
Write the equivalent expression in the simplest form :
-3(x+4) - 5x + 9
-8x-3
Tyler ran 10 miles so far this month. For the rest of the month, he plans to run the same number of miles each day. There are 15 days left. Before the end of the month, Tyler needs to run at least 40 miles to meet his goal.
15m - 10 is greater than or equal to 40
15m - 10 > or = 40
Jasiah spent a total of $84.60 purchasing 12 hats online. There was a one-time shipping
fee of $6.60. The cost of each hat was the same, including tax. Write an equation that can be
used to determine h, the cost of each hat. Then find the cost of one hat.
84.60 = 12h + 6.60
h = 6.50
12 - 1/3x = 8
x = 12
Ms.R has $20.00 to spend on snacks and drinks. She buys one drink for $2.80. Each
snack costs $1.20. Write, solve, and graph an inequality to determine the greatest number of
snacks, s, that Ms.R can buy.
(worth 700 pts)
2.80 + 1.2s = 20
s < or = 14 1/3