2 Step inequalities and Equations

Marchetti/Roop- 7th Grade Inequalities and Equations

​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.

​1) add or subtract - whatever the inverse is of the constant

​2) multiply or divide - whatever the inverse operation is of the coefficient

Multiple Choice

What is the opposite of multiplication?

• Addition

• Subtraction

• Division

Multiple Choice

What is the opposite of addition?

• Subtraction

• Multiplication

• Division

Multiple Choice

What would a graph look like for this solution:

x > 10

• Open circle; shaded to the right

• Open circle; shaded to the left

• Closed circle; shaded to the right

• Closed circle; shaded to the left

Multiple Choice

What would the graph look like for your solution?

x < 50

• Open circle; shaded to the right

• Closed circle; shaded to the right

• Closed circle; shaded to the left

• Open circle; shaded to the left

Multiple Choice

$$x\ \ge\ -5$$  

What would the graph look like for your solution?

• Closed circle; shaded to the left

• Closed circle: shaded to the right

• Open circle; shaded to the right

• Open circle; shaded to the left

Multiple Choice

When graphing an inequality, you use a closed circle when you use which symbols?

• ≤, ≥

• <, >

Multiple Choice

When graphing an inequality, you use an open dot when you use which symbol?

• <, >

• ≤, ≥ 

Multiple Choice

What inequality does the number line graph represent?

• $$x\le-4$$  

• $$x\ge-4$$  

• x < -4

• x < 4

Multiple Choice

What inequality does the number line graph represent?

• $$x\ge3$$  

• x > 3

• x < -3

• $$x\le3$$  

​Two Step Inequalities

​Solving Two Step Inequalities

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

Multiple Choice

You flip an inequality symbol when you...

• subtract

• multiply and divide only

• multiple by a negative number

• multiple or divide by a negative number

Multiple Choice

Does the sign need to flip when solving?
-2x ≥ 22

• YES

• NO

Multiple Choice

Do I need to flip my sign?
3x  ≥ 12

• Yes

• No

Multiple Choice

Solve for t.

6t + 4 ≤ -2

• t ≤ -1 

• t ≤ 1

• t=1

• 1=t

Multiple Choice

Solve for k. 

7k – 2 ≥ -9

• k ≤ -1

• k≤1

• k≥1

• k ≥ -1

Multiple Choice

Solve for u. 
u/7 – 1 ≤ 1

• 14≥u

• 14≤u

• u≤14

• u ≤ -14

Multiple Choice

-3y + 2 > 11

• y < -3

• y > -3

• y < 3

• y > 3

Multiple Choice

22 < 6c + 4

• 11>c

• 3>c

• 11<c

• 3<c

Multiple Choice

Amara will run more than 26 miles this week. So far, she has run 17 miles. What are the possible numbers of additional miles she will run?

Write an inequality to determine the number of additional miles she will run. Use t for the number of additional miles.

• $$t\ +\ 17<26$$  

• $$t+17\ >26$$  

• $$17t<26$$  

• $$17t>26$$  

Multiple Choice

Amara will run more than 26 miles this week. So far, she has run 17 miles. What are the possible numbers of additional miles she will run?

What are the possible number of additional miles that she will run?

• $$t<9$$  

• $$t>9$$  

• $$t\le9$$  

• $$t\ge9$$  

Multiple Choice

Matthew buys candy that costs $8 per pound. He will buy at most 7 pounds of candy. What are the possible amounts he will spend on candy?

Write an inequality to determine the amount (in dollars) Matthew will spend on candy. Use c for the amount (in dollars) Dante will spend on candy.

• $$7c\le8$$  

• $$7c\ge8$$  

• $$8c\ge7$$  

• $$8c\le7$$  

Multiple Choice

Which equation would describe "two times a number plus five equals 15"?

• x + 5 = 15
• 2x + 5=15
• x + 2(5) = 15
• 2(x + 5) = 15

Multiple Choice

The steps in solving 5b - 6 = 24 are: 

• Add 6 to both sides and divide both sides by 5
• Add 6 to both sides and multiply both sides by 5
• Subtract 6 from both sides then multiply both sides by 5
• Subtract 6 from both sides then divide both sides by 5

Multiple Choice

Scott works on cars. He charges $35 for each car plus $7 per hour. Write an equation that represents this scenario if Kylie's car bill was $63.

• 7x + 35 = 63
• 7x = 63
• 7x - 35 = 63
• 35x + 7 = 63

Multiple Choice

WRITE AN EQUATION

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?

• 24-10=7x

• 24+7x=10

• 10+7x=24

• 10+x=14