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 + (
·
) + (
·
)
Great job!
Multiply within each set of parentheses to write another equivalent expression.
19 - 7(2x - 3 )

= 19 + −7(2x + -3)

= 19 + (-7 · 2x) + (-7 · -3)

= 19 +
+
Great job!
Rewrite the expression using fewer terms.
19 - 7(2x - 3)

= 19 + −7(2x + -3)

= 19 + (-7 · 2x) + (-7 · -3)

= 19 + (−14x) + 21

=
+

Answer 1

Let's rewrite the expression step by step as you described:

Starting with the original expression: \[ 19 - 7(2x - 3) \]

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

2. Apply the distributive property: \[ 19 + (-7)(2x) + (-7)(-3) \]

3. Multiply within each set of parentheses: \[ 19 + (-14x) + 21 \]

4. Combine like terms to rewrite the expression using fewer terms: \[ 19 + 21 - 14x \] \[ = 40 - 14x \]

So, the final equivalent expression is: \[ 40 - 14x \]