Answers 7th Grade Math CR Summer SchoolSolving Two-Step Inequalities

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Simon is trying to figure out how much it will cost to buy 30 cases of water for a school picnic. How much will Simon pay for 30 cases of water? Water Prices by the CaseNumber of casesPrice in dollars1566.002088.0035154.00

$99.00

$119.00

$121.00

$132.00

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The first step to solve the equation is shown below.Which property was applied in this step?

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

Which equation, when solved, results in a different value of x than the other three?

8.3 = negative 0.6 x + 11.3

11.3 = 8.3 + 0.6 x

11.3 minus 0.6 x = 8.3

8.3 minus 0.6 x = 11.3

The unchanging value of the ratio between two proportional quantities is

the constant of proportionality.

the constant rate.

the x-value of an ordered pair.

the y-value of an ordered pair.

What is the value of ?

–6

–2

Arnob, Bella, Colin, Dante, and Erin are going to a baseball game. They have a total budget of $100.00 to spend. Each game ticket costs $17.50 and each drink costs $2.00. The inequality below relates x, the number of drinks the 5 friends could buy in all, with their ticket costs and budget.Which best describes the restrictions on the number of drinks they can buy?

They can buy only from 0 to 3 drinks, but no more.

They can buy only from 0 to 6 drinks, but no more.

They can buy only from 0 to 7 drinks, but no more.

They can buy only from 0 to 12 drinks, but no more.

What is the value of ?

Negative 20

Negative 4

Which graph shows the solution set for ?

A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.

A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded.

A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the left of the circle is shaded.

A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the right of the circle is shaded.

What is the value of x in the equation ?

–22

–1.1

1.1

What is the product?

–82

–72

Which expression has a negative value?

2 + 12

(negative 3) (negative 8)

10 minus (negative 18)

Negative 35 divided by 5

What is another way to write the equation ?

7 (StartFraction x over 8 EndFraction) + three-fourths = negative 6

StartFraction 7 + 3 over 8 + 4 EndFraction x = negative 6

StartFraction 7 over 8 EndFraction + three-fourths x = negative 6

StartFraction 7 over 8 EndFraction x minus three-fourths = 6

Based on the table, what is the unit rate for one gallon of gasoline?GasolineNumber of gallonsPrice2$6.603$9.904$13.20

$3.30

$4.60

$5.60

$6.50

The constant of proportionality for the amount of electricity in kilowatt hours and the cost per kilowatt hour is $0.11. Which graph models this situation?

A line graph titled Electricity Cost has Kilowatt hours on the x-axis and Cost in dollars on the y-axis. 100 Kilowatt hours is 11 dollars; 250, 27 dollars and 50 cents.

A line graph titled Electricity Cost has Kilowatt hours on the x-axis and Cost in dollars on the y-axis. 100 Kilowatt hours is 9 dollars; 250, 22 dollars and 50 cents.

A line graph titled Electricity Cost has Kilowatt hours on the x-axis and Cost in dollars on the y-axis. 100 Kilowatt hours is 12 dollars; 250, 30 dollars.

A line graph titled Electricity Cost has Kilowatt hours on the x-axis and Cost in dollars on the y-axis. 100 Kilowatt hours is 13 dollars; 250, 32 dollars and 50 cents.

What is the solution to ?

x less-than-or-equal-to 3

x less-than-or-equal-to 6

x less-than-or-equal-to 48

x less-than-or-equal-to 96

What is the solution to ?

x less-than 2

x less-than 8

x less-than 10

x less-than 40

This table represents the proportional relationship between the number of boxes and the number of magnetic cubes held by the boxes. CubesBoxesNumber of cubes1n562581,000What is the unknown value representing the unit rate?

125

140

156

Using the order of operations, what should be done first to evaluate ?

Divide 12 by 5.

Multiply –6 and 3.

Divide 12 by –6.

Add 3 and –2.

Which table of values corresponds to the graph below?

A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, 0, 3, 6. Column 2 is labeled y with entries negative 1, 0, 1, 2.

A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 2. Column 2 is labeled y with entries negative 3, 0, 3, 6.

A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 6. Column 2 is labeled y with entries negative 1, 0, 1, 2.

A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 2. Column 2 is labeled y with entries negative 1, 0, 1, 6.

The height of a window is 0.6 feet less than 2.5 times its width. If the height of the window is 4.9 feet, which equation can be used to determine x, the width of the window?

2.5 x + 0.6 = 4.9

2.5 x minus 0.6 = 4.9

0.6 x + 2.5 = 4.9

0.6 x minus 2.5 = 4.9

An animal shelter estimates that it costs about $6 per day to care for each dog. If y represents the total cost of caring for a single dog for x days, which table models the situation?

A 2-column table with 3 rows. Column 1 is labeled x with entries 12, 15, 18. Column 2 is labeled y with entries 6, 9, 12.

A 2-column table with 3 rows. Column 1 is labeled x with entries 6, 9, 12. Column 2 is labeled y with entries 12, 15, 18.

A 2-column table with 3 rows. Column 1 is labeled x with entries 36, 54, 72. Column 2 is labeled y with entries 6, 9, 12.

A 2-column table with 3 rows. Column 1 is labeled x with entries 6, 9, 12. Column 2 is labeled y with entries 36, 54, 72.

Sandy evaluated the expression below. What was Sandy’s error?

Sandy should have evaluated as –8.

Sandy should have not multiplied 5 and 5.

Sandy did not add 2 and 3 correctly.

Sandy should have not subtracted 3 from 6 first.

There are 16 tablespoons in one cup. Which table correctly relates the number of cups to the number of tablespoons?

A 2-column table with 4 rows. Column 1 is labeled cups with entries 1, 2, 4, 8. Column 2 is labeled tablespoons with entries 16, 32, 64, 128.

A 2-column table with 4 rows. Column 1 is labeled cups with entries 16, 32, 64, 128. Column 2 is labeled tablespoons with entries 1, 2, 4, 8.

A 2-column table with 4 rows. Column 1 is labeled cups with entries 32, 48, 80, 144. Column 2 is labeled tablespoons with entries 16, 32, 64, 128.

A 2-column table with 4 rows. Column 1 is labeled cups with entries 16, 32, 64, 128. Column 2 is labeled tablespoons with entries 32, 48, 80, 144.

Which equations have the same value of x as ? Select three options.

18 x minus 15 = 72

50 x minus 25 = 72

18 x minus 9 = 72

3 (6 x minus 3) = 72

x = 4.5

Sharon graphed the formula for converting weight from kilograms to pounds.If an item weighs 45 kilograms, what is its weight in pounds?

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