Solving Equations
#1) 5x-4=36
x=8
#13) The second side of a triangle is triple the first side.
3x
17. The width of a rectangle is three less than double the length. What are the correct let statements for the word problem?
Let x be the length
Let 2x-3 be the width
11. Raelyn rents a car for a day. The car costs 15 dollars per day and a one time 20 dollar reservation. If she spent 300 dollars, which of the following equations represents the situation?
15x+20=300
Supplementary angles add up to and are in what shape
180
straight line
#2) 3x + 10 + x = 54
x=11
#13) The third side of a triangle is two more than twice the first side.
2x+2
15. Matt is constructing a fence around the garden in his yard.
The garden has a perimeter of 180 feet. The gate takes up x feet. Solve to and the value of x.
x+45+x+45+15+15=180
2x+120=180
x=15
7. Kyla must pay $10 to rent rollerblades and an additional $2 for every hour she uses them. If Kyla spent $65 in one day, how many hours did Kyla rollerblade for?
10+2x=65
x=27.5
Vertical angles are
equal
bow tie
#5) 6(x − 4) = 36
#12) Three times the difference of a number and 2
3(x-2)
#9) The width of a rectangle is three times the length. If the perimeter of the rectangle is 64, what are the dimensions of the rectangle?
3x+3x+x+x=64
x=8
Length: 8
Width: 24
14)
Harper took an uber home from the train station. The uber charged her a $5 rush hour fee and then $2 per mile. The total fare was $35. Write and solve an equation for the number of miles that Harper drove.
5+2x=35
x=15
10. Write an equation based on the diagrams provided and then solve for the missing variable:
a.)
4y-42=2y
-42=-2y
21=y
#6) 2x − 11 = 3x − 17
x=6
#9) The width is three times the length.
What expression would represent the width?
3x
13. The second side of a triangle is triple the first side. The third side of a triangle is two more than twice the first side. If the perimeter of the triangle is 26, find the dimensions.
x+3x+2x+2=26
6x+2=26
x=4
4, 12, 10
16. Find the mistake in the equation below. Write why the equation is incorrect.
They did not subtract 4x from 8x.
10. Write an equation based on the diagrams provided and then solve for the missing
variable:
b.
6x+12x=180
x=10
#3) 5x − 2(x + 5) = 40
x=16.666
#8)
Four times the sum of twice a number and ten is 40.
4 (2x+10) = 40
13. The second side of a triangle is triple the first side. The third side of a triangle is two more than twice the first side.
WRITE THE LET STATEMENTS
Let x be the first side
Let 3x be the second side
Let 2x+2 be the third side
16. Find the mistake in the equation below. Write why the equation is incorrect then solve it correctly.
4x+7=8x-9
7=4x-9
x=4
10. Write an equation based on the diagrams provided and then solve for the missing
variable:
c)
x-7+43=90
x=54