Introduction to Equivalent Expressions (Math Masters)

5x + 7x + 9y is equal to what?

• 5x + 9y

• 14x + 9y

• 12x + 9y

• 12x + 7y

Answer explanation

To simplify 5x + 7x + 9y, combine like terms: 5x + 7x = 12x. The expression becomes 12x + 9y, which matches the correct answer choice.

Which expression is equivalent to 4(3x + 8y - 2)?

• 12x + 32y - 8

• 12x + 32y + 8

• 12x + 16y - 2

• 4(3x + 8y)

Answer explanation

To simplify 4(3x + 8y - 2), distribute 4: 4*3x + 4*8y + 4*(-2) = 12x + 32y - 8. Thus, the equivalent expression is 12x + 32y - 8, which is the correct answer.

Which expression is equivalent to 12x + 18y?

• 2(5x + 9y)

• 12(x + 5y)

• 3(4x + 5y)

• 6(2x + 3y)

Answer explanation

To simplify 12x + 18y, factor out the greatest common factor, which is 6. This gives us 6(2x + 3y), making it the equivalent expression. The other options do not simplify to match 12x + 18y.

Which expression is equivalent to 3x + 9x + 2y + 8?

• 12x + 8

• 12x + 2y + 8

• 3x + 9y + 8

• 10x + 2y + 8

Answer explanation

To simplify 3x + 9x + 2y + 8, combine like terms: 3x + 9x = 12x. The expression becomes 12x + 2y + 8, which matches the correct answer choice.

Which expression is equivalent to 6(2x + 8y + 3)?

• 12x + 36y + 12

• 3x + 12y + 6

• 12x + 48y + 18

• 6x + 24y + 9

Answer explanation

To simplify 6(2x + 8y + 3), distribute 6: 6*2x = 12x, 6*8y = 48y, and 6*3 = 18. Thus, the expression simplifies to 12x + 48y + 18, which matches the correct answer.

2y + (x + y) is equal to what?

• 3y + x

• 2x + y

• x + 2y

• 3x + y

Answer explanation

To simplify 2y + (x + y), combine like terms: 2y + y = 3y. Thus, the expression becomes 3y + x, which matches the correct answer choice.

Which expression is equivalent to 4(4x + 5)?

• 16x + 20

• 4x + 5

• 8x + 10

• 16x + 15

Answer explanation

To simplify 4(4x + 5), distribute 4 to both terms: 4 * 4x = 16x and 4 * 5 = 20. Thus, the expression becomes 16x + 20, which matches the correct answer choice.

Is 4x + 6y equivalent to 2(2x + 3y)?

• True

• False

Answer explanation

To check if 4x + 6y is equivalent to 2(2x + 3y), distribute the 2: 2(2x) + 2(3y) = 4x + 6y. Since both expressions are equal, the statement is true.

Is 18y - 12x equivalent to 4(4y - 3x)?

• True

• False

Answer explanation

To check if 18y - 12x is equivalent to 4(4y - 3x), expand the right side: 4(4y - 3x) = 16y - 12x. Since 18y is not equal to 16y, the expressions are not equivalent. Therefore, the answer is False.

Which expression is equivalent to 7(3x + 2y + 9) + 4x?

• 25x + 14y + 63

• 14x + 4y + 18

• 7x + 2y + 9

• 21x + 6y + 63

Answer explanation

To simplify 7(3x + 2y + 9) + 4x, distribute 7 to get 21x + 14y + 63, then add 4x to get 25x + 14y + 63. Thus, the correct expression is 25x + 14y + 63.