Solving Two-Step Inequalities Ch6 Lesson 8

​Solving Two-Step Inequalities

7th Grade: ​Chapter 6 Lesson 8

​Two Step Inequalities

​Solving Two Step Inequalities

• The variable must be alone or isolated on one side of the inequality.

• Isolate the variable by using inverse or opposite operations. ​

• Whatever you do to one side ​you must do to the other.

​Two Step Inequalities

​Solving Two Step Inequalities

• When you multiply or divide BY a negative number, the inequality sign is flipped.

Match

Match each phrase with the correct symbol.

• $$>$$  

• $$\ge$$  

• $$\le$$  

• $$<$$  

• $$\ne$$  

greater than

greater than or equal to

less than or equal to

less than

not equal to

• greater than

• greater than or equal to

• less than or equal to

• less than

• not equal to

​Open Circle
--Solution has the < or the > sign.

--The number in the solution will ​not be included in the solution set.
​Closed Circle
--Solution has the < or the > sign. ​

--The number in the solution will be included in the solution set. ​

​Graphing Inequalities​
​When graphing inequalities, the arrow should point toward the possible solutions.

​x > 6 or 6 < x

means x is any number that is greater than 6.

Drag and Drop

When graphing inequalities:

Use an open circle for ​​

Placeholder

.

Use a closed circle for ​​​​

Placeholder

.

Drag these tiles and drop them in the correct blank above

> or <

≥ or ≤

Match

Match each statement with the correct graph.

y < 6

y > 6

y ≤ 6

y ≥ 6

• y < 6

• y > 6

• y ≤ 6

• y ≥ 6

Multiple Choice

Which graph matches the inequality $$-5x\ge-15$$  ?

​If you multiply or divide both sides by a negative number, you must flip the inequality symbol.

Solve like an equation by isolating the variable on one side of the inequality.

​Solve Two-Step Inequalities

-2x + 3 > 9
-3 -3

​-2x > 6
-2 -2

x < -3​

Multiple Choice

True or False:

10 + 3k < 22

Answers in the solution set will be negative

• True

• False

Drag and Drop

When solving inequalities, if you multiply or​ ​

Placeholder

both sides by a ​

Placeholder

number, you must ​

Placeholder

the ​

Placeholder

symbol.

Drag these tiles and drop them in the correct blank above

divide

negative

flip

inequality

add

positive

equal

Multiple Choice

Solve.

$$3n+3\ge30$$  

• $$n\le9$$  

• $$n\ge9$$  

• $$n\le11$$  

• $$n\ge11$$  

Multiple Choice

Solve.

$$-8x+7<15$$  

• $$x>1$$  

• $$x<1$$  

• $$x>-1$$  

• $$x<-1$$  

Multiple Choice

Solve.

$$17\le-2m-3$$  

• $$-10\ge m$$  

• $$-10\le m$$  

• $$-7\ge m$$  

• $$-7\le m$$  

Multiple Choice

Solve and graph the inequality.
77 ≤ 5 + 8n

• A 

• B 

• C 

• D 

Multiple Choice

Solve the inequality $$18<\frac{x}{4}-2$$  

• 80 < x

• $$5<x$$   

• $$4<x$$  

• $$64<x$$  

Draw

Solve the inequality. Graph the solution set on the number line.

Draw

Solve the inequality. Graph the solution set on the number line.

Open Ended

WRITE and SOLVE an inequality for the following sentence. Three times a number increased by four is less than -62.

Open Ended

Answer all parts of this question.