Answers Math 8Analyzing Solutions

Analyzing Solutions — Unit test Answers

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Carlton is solving a linear equation using the steps shown.Equation: Step 1: Add 4x to both sides: Step 2: Combine like terms: What is the next step he needs to complete in order to solve the equation?

Add –2 to both sides of the equation.

Subtract –2 from both sides of the equation.

Multiply each side of the equation by –2.

Divide each side of the equation by –2.

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After getting 5 new rocks, George gave half of his rock collection to Susan. If George gave Susan 36 rocks, which equation could be used to determine how many rocks George started with?

One-half x = 36 + 5

One-half (x minus 5) = 36

One-half (x + 5) = 36

One-half x + 5 = 36

Jeremy wants to determine the number of solutions for the equation below without actually solving the equation.Which method should Jeremy use?

Determine whether the equation has the form , and if it does, the equation has infinitely many solutions.

Determine whether the equation has the form , and if it does, the equation has no solution.

Determine whether the equation has the form , and if it does, the equation has one solution.

Determine whether the equation has the form , and if it does, the equation has no solution.

What is the value of x in the equation ?

–22

–2

Solve the equation using the distributive property and properties of equality.What is the value of x?

7 and one-half

14 and one-half

Oksana wrote the equation below on the whiteboard.What is the value of b?

What is the value of x in the equation ?

Answer not available

Which property is used in the first step to solve this equation?

addition property of equality

distributive property

division property of equality

commutative property

The expression on the left side of an equation is shown below.If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the equation?

–6

Negative 6 x

Negative 6 x + 6

Julissa gave out an equal number of oranges to each of the 6 apartments on her floor. If she gave each apartment 5 oranges, how many oranges did Julissa give out in all?

StartFraction 5 Over 6 EndFraction

1 and one-fifth

Leonardo wrote an equation that has an infinite number of solutions. One of the terms in Leonardo’s equation is missing, as shown below.Which could be the missing term that Leonardo put into the box?

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

Which table shows the correct methods used to justify the solution steps?

A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries division property of equality, combine like terms, distributive property, addition property of equality.

A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries distributive property, combine like terms, addition property of equality, division property of equality.

A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries distributive property, addition property of equality, combine like terms division property of equality.

A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries division property of equality, combine like terms, addition property of equality, distributive property.

What is the solution to the equation ?

x = –10

x = –8

x =

Sarita showed the steps to solving the equation. StepsSarita’s SolutionSarita’s Verification1 23 4 5 When Sarita tried to verify her answer, she found it was wrong. Which explains her mistake?

Sarita’s solution is correct. She made an error in her verification.

Sarita was supposed to add the 5 and 7 in the first step.

Sarita added +13 instead of in the fourth step.

Sarita was supposed to use the division property of equality in the third step.

Antoinette solves the linear equation using the steps shown below. Step 1: Step 2: Step 3: Step 4: She checks her solution by substituting –7 for x in the original equation. She determines that her answer is incorrect. Which best describes Antoinette’s error?

She distributed incorrectly.

She incorrectly combined like terms.

She incorrectly applied the addition and subtraction properties of equality.

She incorrectly applied the multiplication and division properties of equality.

Zahra wants the equation below to have an infinite number of solutions when the missing number is placed in the box.Which number should she place in the box?