Solving with the Distributive Property — Quiz

Question 3 • Mathematics 8

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

Answer

Table with 2 columns and 5 rows.Row 1: Column 1, 'Solution Step'; Column 2, 'Method to Justify' Row 2: Column 1, '3 x minus 15 plus 7 x is equal to 65'; Column 2, 'distributive property' Row 3: Column 1, '10 x minus 15 is equal to 65'; Column 2, 'addition property of equality' Row 4: Column 1, '10 x is equal to 80'; Column 2, 'combine like terms' Row 5: Column 1, 'x is equal to 8'; Column 2, 'division property of equality'

Table with 2 columns and 5 rows.Row 1: Column 1, 'Solution Step'; Column 2, 'Method to Justify' Row 2: Column 1, '3 x minus 15 plus 7 x is equal to 65'; Column 2, 'division property of equality' Row 3: Column 1, '10 x minus 15 is equal to 65'; Column 2, 'combine like terms' Row 4: Column 1, '10 x is equal to 80'; Column 2, 'addition property of equality' Row 5: Column 1, 'x is equal to 8'; Column 2, 'distributive property'

Table with 2 columns and 5 rows.Row 1: Column 1, 'Solution Step'; Column 2, 'Method to Justify' Row 2: Column 1, '3 x minus 15 plus 7 x is equal to 65'; Column 2, 'distributive property' Row 3: Column 1, '10 x minus 15 is equal to 65'; Column 2, 'combine like terms' Row 4: Column 1, '10 x is equal to 80'; Column 2, 'addition property of equality' Row 5: Column 1, 'x is equal to 8'; Column 2, 'division property of equality'

Table with 2 columns and 5 rows.Row 1: Column 1, 'Solution Step'; Column 2, 'Method to Justify' Row 2: Column 1, '3 x minus 15 plus 7 x is equal to 65'; Column 2, 'division property of equality' Row 3: Column 1, '10 x minus 15 is equal to 65'; Column 2, 'combine like terms' Row 4: Column 1, '10 x is equal to 80'; Column 2, 'distributive property' Row 5: Column 1, 'x is equal to 8'; Column 2, 'addition property of equality'

Explanation

Distribute 3 across the parentheses to get 3x − 15 + 7x = 65. Combine the like terms 3x and 7x to get 10x − 15 = 65, then add 15 to both sides to get 10x = 80. Finally, divide both sides by 10 to get x = 8. These methods match choice C.

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