Equivalent Expressions
Simplify the expression:
3x+1+2x
5x+1
Sarah has $15 and she spends $2 on each pencil. If she buys x pencils and is left with $3, how many pencils did she buy?
Sarah bought 4 pencils.
Solve the following equation:
2x+5=3x-7
x=12
Solve the inequality:
2x+3<=7
x<=2
Identify the property used:
2(x+4)=2x+8
Distributive Property
Simplify the expression:
4y+7-2y
2y+7
Emily's age plus 8 is equal to 3 times her age minus 2. How old is Emily?
Emily is 5 years old.
Solve the equation:
4(x-2)=3x+6
x=14
Solve the inequality:
4x-5>7
x>3
Provide an example of the Division Property of Equality
Example:
If
a=b, then a/c=b/c
Simplify the expression:
5a-3+2a+8-4
7a+1
A book costs $20 more than two notebooks. If the notebook costs 'n' dollars and the total cost of both items is $50, how much does the notebook cost?
Solve the equation:
5(x+1)-2=3(x+4)
x=4.5
Solve the inequality:
3(x-2)>=2x+4
x>=10
Identify the property used:
2x+8=14 => 2x=6
Subtraction Property of Equality
Write and simplify the expression for the total number of pencils and erasers:
Jenna bought 3 packs of pencils and 2 packs of erasers. Each pack of pencils contains 4x pencils, and each pack of erasers contains 3x erasers. Write an expression for the total number of pencils and erasers Jenna bought. Simplify the expression.
18x
Jack has 3 times as many marbles as Emma. If Jack gives 8 marbles to Emma, he will have twice as many marbles as Emma. How many marbles does Jack have originally?
Jack originally has 72 marbles.
Solve the equation:
3(2x-4)=2(x+5)+4
x=6.5
Solve the inequality:
x<7
Provide an example of the Addition Property of Equality.
If
a=b, then, a+c=b+c
Simplify the expression:
6x-4(2x-3)+5
-2x+17
A rectangle's length is 5 units more than twice its width. If the perimeter of the rectangle is 36 units, what is the length of the rectangle? (Round to two decimal points)
The length of the rectangle is approximately 13.66 units.
Solve the equation:
2(x-3)+4=3(x+1)-5
x=0
Solve the inequality:
2(x+4)-3<=5(x-1)+2
x>=8/3
x>=2.67
What is the name of the property used?
Distributive Property