M6|L21 Combining Like Terms (Part 2)Sign out

Question

Write equivalent expressions.
How could you start to write equivalent expressions?
19 − 7(2x − 3)

Start left to right and subtract 19 − 7 first.

Use the distributive property to distribute the -7 to the values within the parentheses.
Excellent!
Rewriting subtraction using addition can be helpful to keep track of the subtraction symbol when distributing. Start by rewriting this expression using addition.
19 − 7(2x − 3)

= 19 +
(2x +
)
Good work!
Use the distributive property to write an equivalent expression.
19 - 7(2x - 3)

= 19 + −7(2x + -3)

= 19 + (
·
) + (
·
)

Answer 1

To rewrite the expression \( 19 - 7(2x - 3) \) using the distributive property, you can start by rewriting the subtraction as addition. This can be done by expressing the subtraction in terms of a negative:

1. Rewrite the expression using addition: \[ 19 - 7(2x - 3) = 19 + (-7)(2x - 3) \]

2. Now, apply the distributive property to the term \(-7(2x - 3)\): \[ = 19 + (-7)(2x) + (-7)(-3) \]

3. Calculate the products: \[ = 19 - 14x + 21 \]

4. Combine the constant terms \( 19 \) and \( 21 \): \[ = (19 + 21) - 14x \] \[ = 40 - 14x \]

So the equivalent expression for \( 19 - 7(2x - 3) \) is: \[ 40 - 14x \]