Equations and Expressions Review

Expressions, Equations, & Inequalities

Review

Multiple Choice

Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. She also wants to use the gift card to buy some songs. Each song costs $1.29.

Step 1: Identify the key information

• $50= song cost

  $1.29= gift card

  $9.99= number of songs

  n= album cost

• $50= gift card

  $1.29= song cost

  $9.99= album cost

  n= number of songs

• $50= gift card

  $1.29= song cost

  $9.99= number of albums

  n= album cost

• $50= album cost

  $1.29= number of songs

  $9.99= song cost

  n= gift card

Multiple Choice

Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. She also wants to use the gift card to buy some songs. Each song costs $1.29.

Step 2: Identify the max or minimum

• $50 is the maximum amount she can spend

• $50 is the minimum amount she can spend

• $9.99 is the maximum amount she can use

• $9.99 is the maximum amount she can use

Multiple Choice

Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. She also wants to use the gift card to buy some songs. Each song costs $1.29.

Step 3: Set up the inequality

• $$9.99+1.29n\ge50$$

• $$9.99+1.29n\le50$$

• $$9.99−1.29n\ge50$$

• $$9.99−1.29n\le50$$

​Inequalities on

a graph:

Multiple Choice

Which number line shows all the values of x that make the inequality −3x+1<7 true?

• A

• B

• C

• D

Multiple Select

Select all expressions that are equivalent to  $$6x+1−(3x−1)$$ .

• $$6x+1−3x−1$$

• $$6x+−3x+1+1$$

• $$3x+2$$

• $$6x−3x+1−1$$

• $$6x+1+−3x−−1$$

Multiple Choice

At midnight, the temperature in a city was 5 degrees Celsius. The temperature was dropping at a steady rate of 2 degrees Celsius per hour.

Choose the inequality that represents t, the number of hours past midnight, when the temperature was colder than -4 degrees Celsius. 

***Remember the steps: identify key steps, max/minimum, & px+q=r

• $$5t-4>2$$

• $$5-2t<-4$$

• $$2t+4<5$$

• $$4-5t>-4$$

Multiple Choice

At midnight, the temperature in a city was 5 degrees Celsius. The temperature was dropping at a steady rate of 2 degrees Celsius per hour. In the inequality that represents t, the number of hours past midnight, when the temperature was colder than -4 degrees Celsius. 

$$5-2t<-4$$

Explain your reason below:

• 5= hours

  2= city temp

  t= temp drop

  < greater than

  -4= current temp

• 5= temp drop

  2= greater than

  t= temp drop

  < current temp

  -4= city temp

• 5= city temp

  2= temp drop

  t= hours

  < less than

  -4= current temp

• 5= city temp

  2= temp drop

  t= hours

  < less than

  -4= current temp

Multiple Choice

Choose the matching graph to the inequality:

5-2t<-4

• A

• B

• C

• D

Multiple Choice

Expand the inequality $$-\frac{1}{4}\left(-8x+12y\right)$$ to create an equivalent expression.

**hint: distribute using an area model, then simplify (combine like terms).

• $$2x-3y$$

• $$2y+3x$$

• $$2x+3y$$

• $$2y-3x$$

Multiple Choice

Factor the expression $$36a−16$$

**hint: use the "T" chart to find the greatest common factor

• $$4(9a+4)$$

• $$4(9a−4)$$

• $$9(4a−4)$$

• $$9(4a+4)$$

Multiple Choice

Tyler is simplifying the expression  $$6−2x+5+4x$$ . His work is shown in the picture.

Tyler's work is incorrect. Explain the error he made.

• Tyler did inverse operations.

• He combined unlike terms.

Multiple Choice

Simplify the expression $$6−2x+5+4x$$ into two terms.

• $$11+2x$$

• $$4x-9x$$

• $$4x+9x$$

• $$2x+11$$

Multiple Choice

Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less.

Step 1: Identify the key information.

• 14= full car gallons

  0.6= daily gallons used

  1.5= warning light gallons

  d= each day

• 14= full car gallons

  0.6= daily gallons used

  1.5= days to drive

  d= each day

• 14= full car gallons

  0.6= number of days

  1.5= warning light gallons

  d= each day

• 14= full car gallons

  0.6= number of days

  1.5= cost of gas

  d= each day

Multiple Choice

Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less.

What is the maximum or minimum for the inequality before the light comes on?

Step 2: Identify the min/max

• minimum 0.6 gallons

• maximum 14 gallons

• minimum 1.5 gallons

• maximum 0.6 gallons

Multiple Choice

Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less.

Write an inequality to determine the number of days, t  Diego’s father can drive the car without the warning light coming on.

Step 3: Set up the inequality

• $$14−1.5t>0.6$$

• $$1.5−0.6t>14$$

• $$0.6−14t>1.5$$

• $$14−0.6t>1.5$$

Multiple Choice

Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less.

$$14−0.6t>1.5$$

Solve the inequality and explain your answer.

• $$t<20$$

  Diego's dad can drive less than 20 days without the car light coming on.

• $$t>20$$

  Diego's dad can drive more than 20 days without the car light coming on.

• $$t<-20$$

  Diego's dad can drive less than 20 days without the car light coming on.

• $$t>-20$$

  Diego's dad can drive more than 20 days without the car light coming on.