Review:Writing and Solving Linear Equations and Inequalities

Writing and Solving Linear Equations and Inequalities Review

The inequality signs:

• greater than

• less than

• greater than or equal to

• less than or equal to

Word problems have key words that indicate which sign is necessary for the inequality

For example...

Guided Example

Multiple Choice

Which inequality sign represents should be used in word problems with the key word "maximum"

• $<$

• $\le$

• $>$

• $\ge$

Maximum includes the number and anything less than the number

Multiple Choice

Which inequality sign represents should be used in word problems with the key word "at most"

• $<$

• $\le$

• $>$

• $\ge$

"At most" includes the number and anything less than it

Multiple Choice

Which inequality sign represents should be used in word problems with the key word "at least"

• $<$

• $\le$

• $>$

• $\ge$

"At least" includes the numbers and any greater than it

Multiple Choice

Which inequality sign represents should be used in word problems with the key word "no more than"

• $<$

• $\le$

• $>$

• $\ge$

"No more than" includes the number and all less than the number

Multiple Choice

Which inequality sign represents should be used in word problems with the key word "no less than"

• $<$

• $\le$

• $>$

• $\ge$

"No less than" includes the number and all those greater than it

Multiple Choice

Which inequality sign represents should be used in word problems with the key word "minimum"

• $<$

• $\le$

• $>$

• $\ge$

Minimum allows for the number and all those greater than it

Multiple Choice

Which inequality sign represents should be used in word problems with the key word "more than"

• $<$

• $\le$

• $>$

• $\ge$

"More than" does not include the number - only those greater than the number

Multiple Choice

Which inequality sign represents should be used in word problems with the key word "below"

• $<$

• $\le$

• $>$

• $\ge$

"Below" does not include the number - only those less than the number

In order to write the inequality you must find key words to determine:

• which inequality sign is needed

• the rate of change (is multiplied by x)

• the one time or beginning value (positive or negative)

Try Now Problems

Multiple Choice

Amahl sells candy bars for a band fundraiser that cost $1.50 per candy bar. She purchased 4 boxes at $50 each.

What expression represents the amount of money she collects for the fundraiser?

• 50x

• 1.50x

The amount of money collected is the cost of bars times the number of bars

  $\text{1.50}\cdot x$  

Multiple Choice

Amahl sells candy bars for a band fundraiser that cost $1.50 per candy bar. She purchased 4 boxes at $50 each.

What represents the total cost of the 4 boxes she purchased for the fundraiser?

• 200

• 50

• 4

4 boxes at $50 costs a total of $200

4 x $50 = $200

Multiple Choice

Amahl sells candy bars for a band fundraiser that cost $1.50 per candy bar. She purchased 4 boxes at $50 each.

Profit = Money Collected - Cost

Which expression represents the profit in the scernario above?

• 1.50x - 200

• 1.50x - 50

• 1.50x + 200

Amahl sells candy bars for a band fundraiser that cost $1.50 per candy bar. She purchased 4 boxes at $50 each.

Profit = Money Collected - Cost

Profit = 1.50x - 200

Multiple Choice

Amahl sells candy bars for a band fundraiser that cost $1.50 per candy bar. She purchased 4 boxes at $50 each.

If Amahl needs to make at least $400, then how many candy bars must she sell?

Which inequality represents this scenario?

• 1.50x - 200 < 400

• 1.50x - 200 > 400

"At least" means you need > 400 with that profit expression

Multiple Select

Amahl sells candy bars for a band fundraiser that cost $1.50 per candy bar. She purchased 4 boxes at $50 each.

Amahl needs to make at least $400

Check all answers below that would leave Amahl with at least $400

• 382 bars

• 398 bars

• 400 bars

• 404 bars

Two possible ways to answer this question:

#1 Solve the inequality and see if the choice is within the solution set

#2 Test each choice in the inequality to see if it holds true (this is known as guess and check)

Try Now

Multiple Choice

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant.

The committee wants to keep the total cost no more than $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

• 125x + 55 ≤ 600

• 125x + 55 < 600

• 125x + 55 > 600

• 125x + 55 > 600

Fill in the Blank

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant.

The committee wants to keep the total cost no more than $600. How many hours can the DJ be at the party?

125x + 55 ≤ 600

125x + 55 ≤ 600

125x ≤ 545

x ≤ 4.36

So there is enough for 4 hours

Fill in the Blank

Ty and Jay go to block island for the day and decide to rent mopeds to get around the island. The mopeds can be rented for $50 a day plus an additional $2 for each mile driven.

This can be represented by y = 2x + 50

How much would it cost Jay if he rented a moped for a day and drove 12 miles?

Substitute 12 into the x of y = 2x + 50 since x represents miles

y = 2(12) + 50 = 24 + 50 = 74

So it costs $74