Unit Test — Unit test Answers

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What is the value of k in the equation ?

11 and one-third

102

117

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Which is the most efficient first step to solve for x in the equation ?

Add 3.7x to both sides of the equation.

Add 4.3x to both sides of the equation.

Subtract 18 from both sides of the equation.

Subtract 34 from both sides of the equation.

Which equation is equivalent to ?

Negative StartFraction 5 Over 6 EndFraction = one-fourth x + one-fourth

Two-thirds x = negative StartFraction 5 Over 12 EndFraction x minus StartFraction 7 Over 12 EndFraction

One-fourth x minus StartFraction 5 Over 6 EndFraction = one-fourth

Two-thirds x minus StartFraction 13 Over 12 EndFraction = negative StartFraction 5 Over 12 EndFraction x

Jared wrote an equation for the perimeter of an equilateral triangle as 3x = 20. What does x represent in his equation?

perimeter of the triangle

area of the triangle

side length of the triangle

height of the triangle

The equation is written in standard form. What is the first step when solving for x?

Add 5x to both sides of the equation.

Subtract 5x from both sides of the equation.

Add 10y to both sides of the equation.

Subtract 10y from both sides of the equation.

What is the least common denominator of the equation ?

Jorge solves the equation using the steps below. Step 1: Step 2: Step 3: Step 4: Step 5: Jorge verifies his solution by substituting into the original equation for x. He determines that his solution is incorrect. Which best describes Jorge’s error?

Jorge distributed incorrectly.

Jorge incorrectly combined like terms.

Jorge incorrectly applied the addition and subtraction properties of equality.

Jorge incorrectly applied the multiplication and division properties of equality.

Horatio is solving the equation . Which equations represent possible ways to begin solving for x? Check all that apply.

Two-fifths x = StartFraction 7 Over 20 EndFraction x + one-fourth

Two-fifths x = StartFraction 7 Over 20 EndFraction x + five-fourths

Negative three-fourths = negative StartFraction 1 Over 20 EndFraction x minus one-half

Negative three-fourths = three-fourths x minus one-half

Negative three-fourths + StartFraction 1 Over 20 EndFraction x = negative one-half

Shau-uen solved the equation . Her work is shown below.Step 1Step 2Step 3Step 4In which step did Shau-uen make her first error?

Step 1

Step 2

Step 3

Step 4

Misha solves the equation by applying the distributive property to each side of the equation. The result is . Misha then wants to combine like terms. Which are the terms Misha should combine?

3x – 2x and –8 – 7

3x – 2x and 8 – 7

3x – 2x + 4x and –6 – 8 – 7

3x – 2x – 6 and 4x – 8 – 7

A regular hexagon and a rectangle have the same perimeter, P. A side of the hexagon is 4 less than the length, l, of the rectangle. The width of the rectangle, w, is 2 less than the length of the rectangle. What is the perimeter of the hexagon?

Answer not available

Candice wrote the four equations below. She examined them, without solving them, to determine which equation has an infinite number of solutions.Which of Candice’s equations has an infinite number of solutions?

Negative 5 x + 1 = negative 5 x + 1

Negative 2 x + 1 = negative 2 x + 2

3 x + 5 = 3 x minus 5

4 x minus 2 = x + 1

What is the value of x in the equation ?

Isaac wants the equation below to have no solution when the missing number is placed in the box.Which number should he place in the box?

Consider the solution to the linear equation. Which describes the inverse operations used after the distributive property?

addition then division

subtraction then division

multiplication then subtraction

division then addition

Three more than twice the sum of a number and half the number equals 105. Which equation models this relationship?

2 (x + one-half x) + 3 = 105

2 x + one-half x + 3 = 105

2 x + 3 = one-half x + 105

2 (x + 3) = one-half x + 105

Mr. Lopez wrote the equation on the board. Four students explained how to solve for g.Alyssa: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then subtracted 30 from 150 to find the value of g, which is 120.” Rahul: “I added 32, 8, and 10 to get 50, and then I subtracted 150 to find the value of g, which is –100.” Toni: “I subtracted 18 from 32 to get 14, which I then divided into 150 to find the value of g, which is .” Wilhem: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then divided both sides by 30 to find the value of g, which is 5.” Which student’s work is correct?

Alyssa

Rahul

Toni

Wilhem

Maricella solves for x in the equation . She begins by adding –4 + 4 on the left side of the equation and 1 + 1 on the right side of the equation. Which best explains why Maricella’s strategy is incorrect?

The multiplication that takes place while distributing comes before addition and subtraction in order of operations.

In order to combine like terms on one side of the equation, the inverse operation must be used.

When the problem is worked in the correct order, the numbers that Maricella added are not actually like terms.

Maricella did not combine all three constants on both sides of the equation; she combined only two.

Erin is a dog groomer. She charges a $6.00 base fee plus an extra $0.50 per pound. If x represents the weight of the dog in pounds, which equation models her income for each dog groomed?

Income = 0.5 x + 6