Simplifying
Simplify the following expressions
5x(-3+7)
-15x+35
Solve the following equation
4x-7=21
x=7
Determine how many solutions
3x+5=2x+8
One solution
Sam bought 3 movie tickets and spent $27. If each ticket cost the same and he also paid a $3 service fee, how much was each ticket? Write the equation and solve.
3x + 3 = 27, x = $8
Define distribute
to multiply a group of something (parenthesis)
-9(-3x+23+2m)
27x-207-18m
Solve for m
-5m+10=-5
m=3
Determine how many solutions
5x−3=5x+7
No solution
Mia earns $5 per chore she completes, plus a $10 weekly allowance. If she earned $40 last week, how many chores did she complete? Write the equation and solve.
5x + 10 = 40, x = 6 chores
Define combining like terms
Adding or subtracting constants or variables with the same letter
-15x+6-7m-4+4m-3m
-22m+2-10m
Find the value of x
3x−5=2x+4
x=9
Determine how many solutions
2(x+3)=2x+6
Infinite solutions
An online store charges a $6 shipping fee plus $12 per T-shirt. If the total cost was $54, how many T-shirts did Jordan buy? Write the equation and solve.
12x + 6 = 54, x = 4 t-shirts
Identify the constant(s), coefficient(s), and variable(s) below
-10x+7-3m-9
Constants: 7 and -9
Coefficients: -10 and -3
Variables: x and m
15-6(-4z+10)-10z
14z-45
-45+14z
Solve for x
5(x−2)=3(2x+4)+1
x=-23
Determine how many solutions
3x+4−2x=7
One solution
A father is 4 times as old as his son. In 5 years, the father will be 30. How old is the son now? Write the equation and solve.
4x + 5 = 30, x = 6.25 years old
What is the difference between an equation and expression
An equation has an = and can be solved
An expression can only be simplified (in some cases) not solved
12(-3x+13)-5(4x-22)
-56x+266
266-56x
Find the value of x
2(3x−4)−3(2x+1)=5x+7
x=-18/5
Determine how many solutions
3x−5+2x+4=5x−2+6
No solution
You pay a $50 down payment and then $75 per month. If the total after 4 months is $350, how many months are left to pay if the total cost is $650? Write the equation and solve.
75x + 50 = 650 , x = 8 months
What does it mean to simplify
To put something in smallest terms (everything is distributed/combined)