Mastering Expressions and Variables

Answer explanation

To simplify 3(x + 4), apply the distributive property: 3 * x + 3 * 4 = 3x + 12. Thus, the correct answer is 3x + 12.

Answer explanation

To simplify the expression, combine like terms: 5x + 3x - 2x = (5 + 3 - 2)x = 6x. Thus, the correct answer is 6x.

Answer explanation

The phrase "The sum of a number y and 9" indicates that we need to add 9 to the variable y. This is represented algebraically as y + 9, making the correct choice y + 9.

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Answer explanation

To evaluate the expression 2a + 3b, substitute a = 2 and b = 3: 2(2) + 3(3) = 4 + 9 = 13. Thus, the correct answer is 13.

Answer explanation

To combine like terms, group the 'm' terms and the constant terms: (4m - 2m) + (7 + 3) = 2m + 10. Thus, the correct answer is 2m + 10.

Answer explanation

Using the distributive property, multiply 2 by each term inside the parentheses: 2 * 3x = 6x and 2 * -5 = -10. Thus, 2(3x - 5) = 6x - 10, making the correct answer 6x - 10.

Answer explanation

To simplify the expression, combine like terms: 7y - 3y + 2y = (7 - 3 + 2)y = 6y. Thus, the correct answer is 6y.

Answer explanation

The phrase "Twice a number z decreased by 4" translates to 2z - 4. Here, 'twice a number' means multiplying the number z by 2, and 'decreased by 4' means subtracting 4 from that result.

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Answer explanation

Substituting x = 3 and y = 2 into the expression 4x - 3y gives 4(3) - 3(2) = 12 - 6 = 6. Therefore, the correct answer is 6.

Answer explanation

To combine like terms, group the 'p' terms: 9p - 3p = 6p. Then, combine the constant terms: 4 + 6 = 10. Thus, the simplified expression is 6p + 10, which matches the correct answer.