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which of the following answers applies the distributive property of multiplication over addition correctly for simplifying 23 - 9 (2x + 5) + 11x
To apply the distributive property of multiplication over addition correctly in the given expression, we need to distribute the term outside the parentheses to each term inside the parentheses.
The correct application would be:
23 - 9 * 2x - 9 * 5 + 11x.
Simplifying this expression further, we have:
23 - 18x - 45 + 11x.
Combining like terms, we get:
-7x - 22.
Therefore, the correct answer is -7x - 22.
-4 (7b + 3) + 24b - 8
To apply the distributive property of multiplication over addition correctly in this expression, we need to distribute the -4 to every term inside the parentheses.
The correct application would be:
-4 * 7b + (-4) * 3 + 24b - 8.
Simplifying this expression further, we have:
-28b - 12 + 24b - 8.
Combining like terms, we get:
-4b - 20.
Therefore, the correct answer is -4b - 20.
2 (3v + 9) - 14 - 6 (- 5v - 4)
To apply the distributive property of multiplication over addition correctly in this expression, we need to distribute both numbers outside the parentheses to every term inside the parentheses.
The correct application would be:
2 * 3v + 2 * 9 - 14 - 6 * (-5v) - 6 * (-4).
Simplifying this expression further, we have:
6v + 18 - 14 + 30v + 24.
Combining like terms, we get:
36v + 28.
Therefore, the correct answer is 36v + 28.
-15 + 4/5 (15e - 10) - 10e
To apply the distributive property of multiplication over addition correctly in this expression, we need to distribute 4/5 to every term inside the parentheses.
The correct application would be:
-15 + 4/5 * 15e - 4/5 * 10 - 10e.
Simplifying this expression further, we have:
-15 + (4/5) * 15e - (4/5) * 10 - 10e.
Multiplying fractions, we get:
-15 + (12e/5) - (8/5) - 10e.
Combining like terms, we get:
12e/5 - 10e - 23.
Therefore, the correct answer is 12e/5 - 10e - 23.