Equations
3x + 7 = 19
x = 4
2x + 5 < 11
x < 3
Sarah has 5 apples. She buys more so that she ends up with 17 apples. Write an equation to represent this situation.
5 + x = 17
What kind of solution is this?
3x + 5 = x + 13
If it's one solution, find the value of x.
One solution
x = 4
When do you flip the inequality sign?
When we multiply or divide by a negative
2(x + 3) = 14
x = 4
3x - 4 ≥ 8
x ≥ 4
A taxi charges a flat fee of $3 plus $2 per mile. Write an equation for the total cost of a ride that is m miles long.
C = 2m + 3
What kind of solution is this?
7x + 9 = 9 + 7x
If it's one solution, find the value of x.
Many (infinite) solutions
What inequality sign do you use when we have the words "at most"?
≤
4x - 5 = 3x +19
x = 24
-3x + 7 ≤ -5
x ≥ 4
A school bus can hold a maximum of 60 students. If there are already 18 students on the bus, write an inequality to show how many more students can still get on.
x + 18 ≤ 60
What kind of solution is this?
6x + 2 = 6x + 10
If it's one solution, find the value of x.
No solution
The formula for area is A = b * h. Rearrange the formula to solve for h.
h = A/b
x/4 + 5 = 9
x = 16
6(x - 1) ≥ 12
x ≥ 1
A babysitter charges $10 an hour plus a $5 flat fee for gas. Write an equation for the total cost if the babysitter works h hours.
C = 10h + 5
What kind of solution is this?
5(x + 1) = 2x + 14
If it's one solution, find the value of x.
One solution
x = 3
What inequality sign do you use when we have the words "at least"?
≥
6(x - 2) = 3x + 12
x = 8
-3x + 8 ≤ 2x - 7
x ≥ 3
You're saving for a bike that costs $150. You already saved $40 and plan to save $15 each week. Write an inequality to represent how many weeks until you can afford the bike.
40 + 15x ≥ 150
What kind of solution is this?
8x - 3 = 2(4x + 5)
If it's one solution, find the value of x.
No solution
What two key components are needed for an equation?
A variable and an equal sign