2.4 Creating and Solving Inequalities Review

by Grace Gardner

​Solving Inequalities

​In the last lesson we learned that you can solve an inequality the same way as you would solve an equation, with one difference: when you multiply or divide by a negative number, the inequality will reverse.

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The next three questions are about solving inequalities.

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• Simplify both sides of the expression.

• ​Move variable terms to one side of the equation using the properties of equality.

• ​Solve using the properties of equality.

Multiple Choice

-138 ≥ -6(6b − 7)

• b ≤ 5
• b ≤ -5
• b ≥ 5
• b ≥ -5

Multiple Choice

-p − 4p > -10

• p > -2
• p > 2
• p < -2
• p < 2

Multiple Choice

Solve the inequality

• x ≥ -7

• x ≤ -7

• x ≤ -15

• x ≥ -15

​In the first lesson we learned that you plot an inequality on a number line.

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The next three questions are about plotting the solutions of inequalities.

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• > or < open circle because they do not include the value.

• ≥ or ≤ closed circle because they do include the value.

Plotting Inequalities

Multiple Choice

Farah is graphing the inequality . She draws a number line and shades over the numbers that are greater than 4.

What must she do to complete his representation of x > 4?

• Draw an open circle at 4.

• Draw a closed circle at 4.

• Draw an open circle at 5.

• Draw a closed circle at 5.

Multiple Choice

What inequality does the number line graph represent?

• x > 5
• x < −5
• x ≥ 5
• x ≥ −5

Multiple Choice

When you graph an inequality, you use a closed dot when you use which symbols?

• ≤, ≥ 
• <, >
• ≤, <
• ≥, >

Writing Inequalities

​In the first lesson of this module we learned how to pick out key words in order to write an inequality based on word problems.

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The next three questions are about picking out key words in order to write an inequality based on word problems.

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• Use what you learned last class, including the group slides and Jamboards as tools.

Multiple Choice

Layan saved more than $36. Which inequality represents the amount that she saved? 

• s > 36
• s < 36
• s ≤ 36
• s ≥ 36

Multiple Choice

6. J&A Cookies makes a profit of 5.50BHD per Mini Cheescake. If the store wants to make a profit of no less than $5225, how many Mini Cheescakes does it need to sell? 

• x/5.50 ≥ 5225
• 5.50x ≥ 5225
• x + 5.50 ≤ 5225 
• x - 5.50 ≤ 5225

Multiple Choice

Ariana is going water skiing. She can purchase skis for $125 or she can rent skis for $30 an hour. In both cases she must rent a safety flotation device to wear that is $5 per hour. Which inequality shows the number of hours Ariana must ski for the cost of buying skis to be less than renting skis?

• 125 + 5x > 30x

• 125 + 5x < 35x

• 125 + 5x < 30x

• 125 + 5x > 35x