Equations and Inequalities

Inequality Basics

100

Name the four inequality symbols.

>,<,≥,≤

(Greater Than, Less Than, Greater Than or Equal To, Less Than or Equal To)

200

What is the difference between an inequality and an equation?

An inequality uses symbols like >,<,≥,≤ instead of an equals sign and represents a range of solutions.

300

True or False: x≤5 means x can only be 5.

False. x can be 5 or any number less than 5.

400

What happens to the inequality symbol when you multiply or divide by a negative number?

The inequality symbol must be flipped.

500

When graphing inequalities, when do you use an open circle and when do you use a closed circle? Also, explain how to determine which direction to shade.

• Use an open circle for < or > because the number is not included in the solution.
• Use a closed circle for ≤ or≥ because the number is included in the solution.
• If the inequality is greater than (> or ≥), shade to the right.
• If the inequality is less than (< or ≤\le≤), shade to the left.

One-Step Inequalities

100

Solve: x+3<10

x<7

200

Solve: 5x≥20.

x≥4

300

Graph x>−2 on a number line. Should the dot be open or closed?

Open dot at -2, shading to the right.

400

Solve and graph: −3x>9.

x<−3, open dot at -3, shading to the left.

500

Which inequality represents “All numbers less than or equal to 12”?

x≤12

Equation Basics

100

What does it mean to “solve” an equation?

Find the SPECIFIC value of the variable that makes the equation true.

200

Name each operation and its inverse.

Addition- Subtraction

Subtraction-Addition

Multiplication-Division

Division-Multiplication

300

When you multiply or divide by a negative when solving an equation, do you need to flip any signs?

No, that only applies to inequalities and their symbols.

400

Why do we use inverse operations when solving equations?

To isolate the variable and solve for its value.

500

What does it mean to keep an equation balanced?

Whatever you do to one side of the equation, you must do to the other side to keep both sides equal.

One-Step Equations

100

What inverse operation would you use to solve x−3=7?

BE SPECIFIC

Add 3 to both sides.

200

What inverse operation would you use to solve x/4=12?

BE SPECIFIC 

Multiply both sides by 4

300

Solve for x: x+4=9.

x=5

400

Solve for x: 6x=36

x=6

500

Solve for x: x/−5=−7.

x=35

Two-Step Equations

100

Why are two-step equations called TWO-STEP equations?

Because we have to perform inverse operations TWO TIMES.

200

In what order should you undo two-step equations?

First undo addition and subtraction, then undo multiplication and division (reverse pemdas)

300

What is the first step in solving 2x+5=11?

Subtract 5 from both sides.

400

What is the second step in solving 3x−4=8

Divide both sides by 3.

500

Solve: 5x−2=18.

x=4