Unit 3 Slides

Section 1: Linear Expressions

Example 1.

Gracie bought a jacket for d dollars, and then sold it to a clothing store for 15%
more than she paid for it. She used the following expression to calculate how
much money she made in the sale.

0.15d + d

What is another expression that could be used to get the same results?

Example 2.

Simplify the following expression.

(3x + 10y) + (15x + 7y)

Example 3.

Simplify the following expression.

(23x + 45y) - (17x + 32y)

Example 4.

Simplify the following expression.

3(7x + 11) + 14

Example 5.

Factor the expression completely.

-2x + 14

Section 2: Multi-Step Problems

Helpful Hints to Solving Multi-Step Problems

●UNDERSTAND THE PROBLEM

Identify what to solve for in the problem.

Weed out any unnecessary information given.

●DEVISE A PLAN

What steps need to be taken to solve the problem?

Identify the skills that can be applied to solving the problem.

●CARRY OUT THE PLAN

Perform the necessary calculations to solve the problem.

Make sure to answer the question being asked.

●REVIEW YOUR WORK

Does the answer seem reasonable?

Check for careless mistakes.

Example 1.

Three friends are making a 400-mile road trip.

Jack drove ⅕ of the trip, Steve drove 40% of the trip, and Stan drove the rest.

How far did Stan drive?

Example 2.

Susan went shopping. Shirts were ½ off, pants were 20% off, and shoes were
discounted $9.99.

Susan bought one of each item. The original prices were $42.50, $32.00, and
$54.99, respectively.

Not including tax, how much did she spend on all three items?

Example 3.

Dorise needs 1 7/16 cups of water to make cookies and 2 ⅝ cups of water to
make a pitcher of lemonade. About how many cups of water does she need in all?

Example 4.

Estimate 10% of $5.54.

Example 5.

Jack ran 59.2 meters on Monday, 67.6 meters on Tuesday, and 20.9 meters on
Wednesday. About how many meters did he run in these three days?

Example 6.

Evan has $50 in birthday money. He spent $12.87 on a toy and $19.09 on a new
shirt. About how much of his birthday money does Evan have left?

Example 7.

Heather earns between $25.12 and $31.89 each time she babysits. If she babysits
5 times this week, about how much money would she earn?

Example 8.

Fiona spent $312.23 on 6 outfits at the mall. About how much did she spent on
each outfit?

Section 3: Write and Solve Linear
Equations

Example 1.

Translate the following sentence into an equation.

Twice a number decreased by 6 is 10.

Example 2.

Last weekend, Christina bought 7 new pencils. Now, she has 26 pencils total. What
equation could be used to find x, the number of pencils Christina had before last
weekend?

Example 3.

Rhea had $726.48 in her bank account. She paid her rent and bought some
household items. Her account balance now is -$65.34. What equation could be
used to find x, the amount of money she spent on rent and household items?

Example 4.

Tanner went to the movies on Saturday. He spent $8.25 on the movie ticket plus
an additional amount at the snack bar. If Tanner spent a total of $21.20 on his
ticket and snacks at the movies, how much did he spend at the snack bar?

Example 5.

Belinda withdrew $150 from her savings account. This brought the balance of her
savings account to $685.

How much did Belinda have in savings before her withdrawal?

Example 6.

Kandice bought a whole season of her favorite television show on DVD. She
watched all of the episodes back-to-back on Friday. If each episode lasts one-half
hour, and it took her five and a half hours to watch all the episodes, how many
episodes were in the whole season?

Example 7.

Troy won a cash prize from a radio contest and decided to share his winnings
evenly between himself and two of his friends. If each person ended up getting
$115.20, how much was Troy's cash prize?

Example 8.

The average temperature of a city was reported to be -15.25°F last year. If the
average temperature of the city is -12.6°F this year, by how much did the average
temperature change?

Section 4: Write and Solve Linear
Inequalities

Example 1.

The band members at Smith High School must complete at least 1,500 total hours of community service during
the school year. This year, the band students decided to complete all of their community service hours at a local
animal shelter. The animal shelter offers 5-hour work shifts to the band members on weekends.

If during the first semester, the band had a total of 785 community service hours from working at the shelter, write
an expression to represent the number of shifts the band members need to complete during the second semester
of the school year.

Example 2.

Samantha is selling boxes of cookies for a school fundraiser, and she earns $5.00 for each box of
cookies that she sells.

Suppose Samantha must earn at least $250.00 during the fundraiser. She has already made $85.00
selling cookies. If this situation is modeled by the inequality below, how many more boxes of
cookies, b, must Samantha sell to earn at least $250.00?

Example 3.

Josephine is baking cupcakes for a bake sale. Each batch of cupcakes requires
her to use 3 eggs, and there are 15 cupcakes in each batch. She has already baked
one batch.

If Josephine has 21 eggs left, what is the maximum total number of cupcakes that
she can bring to the bake sale?

Graphing Inequalities

●Greater than or equal to: solid line or dot, graph to the positive values up

●Less than or equal to: solid line or dot, graph to the negative values or down

●Greater than: dashed line or open dot, graph to the positive values and up

●Less than: dashed line or open dot, graph the negative values or down

Example 4.

Graph the solution to the following inequality.