Question

The expression 3x - 4(2x - 5) is equivalent to the expression 20 - 5x.
a) True
b) False

Answer 1

false The expression 3x - 4(2x - 5) can be simplified using the distributive property, which states that when you multiply a number by a sum, you can distribute the multiplication to each term inside the parentheses.

Applying this property to the given expression, we get:

3x - 4(2x) + 4(-5)

Multiplying 4 with 2x gives us 8x, and multiplying 4 with -5 gives us -20.

So, the expression becomes:

3x - 8x - 20

Simplifying further, we can combine like terms by subtracting 8x from 3x, which gives us:

-5x - 20

Therefore, the simplified expression is -5x - 20, not 20 - 5x. Hence, the statement "The expression 3x - 4(2x - 5) is equivalent to the expression 20 - 5x" is false.

Answer 2

The expression 3x - 4(2x - 5) is equivalent to the expression 20 - 5x.

Step-by-step explanation:

To determine if the expression 3x - 4(2x - 5) is equivalent to the expression 20 - 5x, we need to simplify both expressions and compare their results.

Starting with 3x - 4(2x - 5), we use the distributive property to multiply -4 by each term inside the parentheses:

3x - 4 * 2x + 4 * 5

This simplifies to: 3x - 8x + 20

Combining like terms, we get: -5x + 20

Now comparing this with the expression 20 - 5x, we can see that they are indeed equivalent. Therefore, the answer is a) True.