Solving with the Distributive Property — Quiz Answers

Sarita showed the steps to solving the equation. 5 times open paren x minus 3 close paren plus 7 times open paren x plus 4 close paren is equal to 73 Steps Sarita’s Solution Sarita’s Verification 1 5 x minus 15 plus 7 x plus 28 is equal to 73 5 times open paren 5 minus 3 close paren plus 7 times open paren 5 plus 4 close paren is equal to 73 5 times negative 2 plus 7 times 9 is equal to 73 negative 10 plus 63 is equal to 73 53 is not equal to 73 2 open paren 5 plus 7 close paren times x plus open paren negative 15 plus 28 close paren is equal to 73 3 12 x plus 13 is equal to 73 4 12 x is equal to 60 5 x is equal to 5 When Sarita tried to verify her answer, she found it was wrong. Which explains her mistake?

Maria solved the equation. 4 times open paren 3 x minus 8 close paren minus 4 is equal to 24 12 x minus 32 minus 4 is equal to 24 12 x minus 36 is equal to 24 12 x is equal to 60 x is equal to 5 What methods did she use and in what order did she use them?

Which table shows the correct methods used to justify the solution steps? 3 times open paren x minus 5 close paren plus 7 x is equal to 65

Solve the equation using the distributive property and properties of equality. 1 half times open paren x plus 6 close paren is equal to 18 What is the value of x ?

Henry showed all the steps he took to solve the equation. 4 times open paren negative 1 half x plus 7 close paren plus 5 x is equal to 15 Step Simplified Expression 1 negative 2 x plus 28 plus 5 x is equal to 15 2 3 x plus 28 is equal to 15 3 3 x is equal to 15 4 x is equal to 5 Sammy tried to verify the solution by substituting x is equal to 5 back into the original equation. It did not result in a true statement. Which explains why Henry’s solution is incorrect?

Paolo is putting a fence around his pool. The length of the pool is 20 feet, the width is open paren 20 minus x close paren feet, and the area of the pool is 300 square feet. Recall that area is length multiplied by width. The equation models the area of the pool. 20 times open paren 20 minus x close paren is equal to 300 What is the value of x ? Round to the units place.

Solve the equation using the distributive property and properties of equality. negative 5 times open paren A plus 3 close paren is equal to negative 55 What is the value of A ?

What is the value of x in the equation? 6 times open paren x minus 8 close paren is equal to 72

Liliana solved the given equation. When she tried to verify her answer, she realized she made an error. 1 third times open paren x plus 18 close paren is equal to 7 1 third x plus 6 is equal to 7 1 third x plus 6 minus 6 is equal to 7 plus 6 1 third x is equal to 1 x is equal to 3 Which correction should Liliana make?

Consider the equation and its solution. 8 times open paren x minus 2 close paren is equal to 64 8 x minus 16 is equal to 64 8 x is equal to 80 x is equal to 10 Which property is used in the last step to find that x is equal to 10 ?