🧩 Simplify It!
Simplify:
3x + 5x
8x
Which expression is equivalent to:
5(x + 2)
A. 5x + 2
B. 5x + 10
C. x + 10
D. 5x + 7
B: 5x+10
-5x + 9 = 24
x=-3
A gym charges a $10 membership fee plus $5 per month. You paid $40.
Write and solve an equation.
5x + 10 = 40
x = 6
6 months
Which property allows you to rewrite:
4(x + 3) → 4x + 12
Distributive Property
Simplify:
7x − 3 + 2x + 8
9x+5
Which expression is equivalent to:
8x − 12
A. 4(2x − 3)
B. 4(2x + 3)
C. 8(x − 12)
D. 2(4x − 12)
A. 4(2x − 3)
-6x – 10 = 20
x=-5
Ms. Fredrick purchased a bottled water for $1.25 and 6 doughnuts. The total cost was
$6.90. Write an equation to determine the cost of a doughnut.
1.25 + 6x = 6.90
Which operation should you undo first when solving:
x + 9 = 17?
Subtract 9
Simplify:
4(2x + 3)
8x+12
8. Simplify the expression by distributing and
then combining like terms.
8y – 1/2 (4y – 16)
6y+8
Solve:
3(x + 4) = 27
x=5
A home improvement store advertises 60 square feet of flooring for $287.00, including an
$80.00 installation fee. Write an equation to represent the cost of one square foot of flooring.
80 + 60x = 287
A student solves:
3x + 5 = 20
by doing:
20 − 5 = 15
15 ÷ 3 = 5
How is the student able to solve the equation?
They are undoing the operations in reverse order.
Simplify:
−3(2x − 5) + 4x
-2x+15
Explain why these expressions are equivalent:
3(x + 4) and 3x + 12
The distributive property was used:
Solve:
−2(x − 5) = 18
x=-4
A rectangle has a perimeter of 54 cm. Its length is 6 cm.
What is its width?
A rectangle has a perimeter of 54 cm. Its length is 6 cm.
What is its width?
Answer:
2(6 + w) = 54
6 + w = 27
w = 21 cm
A student says:
"The expression 2(x + 5) is the same as 2x + 5."
Are they correct? Explain.
No.
2(x + 5) = 2x + 10
The 2 must be distributed to both terms.
Simplify:
2(3x − 4) − 3(x + 5) + 7
3x-16
Which form best reveals that a number has been increased by 25%?
A. x + 25
B. 1.25x
C. x − 0.25x
D. 25x
B. 1.25x
6m + 4(-2m + 6) = 10
m=7
Asher’s sister is eight years older than
Asher. Their combined ages add up to 20.
How old is Asher?
(a+8) + a = 20
Asher is 6
A student solves:
−3(x + 4) = 18
and gets:
x = −2
Is the student correct?
No.
Correct work:
−3(x + 4) = 18
x + 4 = −6
x = −10