Solving Equations and Inequalities, Solving Equations and Inequalities

x = 5

Solve the equation. 6(x - 3) = 12

x ≥ 1

What inequality is shown on this graph?

x = -4

2x - 3 = -11

x = -5

2x - 7 = -17

expression

A mathematical phrase that contains operations, numbers, and/or variables.

equation

A mathematical sentence that shows that two expressions are equivalent

12h + 25 = 120

A shop rents surfboards for $12 per hour plus a $25 daily charge. If Vince rented a bike and the total bill was $120, how many hours (h) did Vince rent the bike? Write an equation to represent this situation. Use h for hours.

inequality

A statement that compares two quantities using <, >, ≤,≥, or ≠

variable

A symbol used to represent a quantity that can change

constant

A term without a variable

80 + 2s = 200

As a salesperson, you are paid $80 per week plus a commission of $2 per sale. This week you want your pay to be $200. Write an equation you could use to find the number of sales you need to make.

12w

Every week James will save $12. Write an expression that could be used to calculate how much money he will save after any number of weeks, w.

46 + n = 98

Janelle had 46 stamps in her collection. She bought several more online. She now has 98 stamps in her collection. Write an equation to represent how many stamps (n) she bought online. Use n for number of stamps.

4n + 2 = 10

Jenna scored ten goals this season. This is 2 more than 4 times the number she scored last season. Write an equation to find out how many goals she scored last season.

x = 2

Solve the equation. -20 = -4x - 6x

x = -5

Solve the equation. -3x - 4x = 35

x = 9

Solve the equation. -9x + 1 = -80

x = 6

Solve the equation. 50 = 5x + 20

x = -11

Solve the equation. 5x + 4 = 3x - 18

x = 2

Solve the equation. 5x - 3 + 3x -3 = 10

x = -4

Solve the equation. 7(2x + 1) = 9x -13

x = 0

Solve the equation. 9x - 7 = -7

x = 1

Solve the equation. x - 1 = 5x + 3x - 8

x ≥ 5

Solve the inequality. -1 + x ≥ 4

x < -8

Solve the inequality. 4x < -32

x ≤ 6

Solve the inequality. 5(6 + 3x) + 7 ≤ 127

x > 6

Solve the inequality. 5x > 30

8 + 2m ≥ 30

You are participating in a fundraising race, and your sponsor has agreed to give you a $8 flat donation, plus $2 per mile (m) that you run. You want to earn at least $30. Write an inequality to represent the number of miles you must run. Use m for number of miles.

Distributive Property

a(b + c) = ab + ac

closed circle

is a solution; is included in the solution set

open circle

not a solution; not included in the solution set

Coefficient

number in front of a variable

x = 15

x - 6 = 9