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 +
+

Answer 1

To continue simplifying the expression \(19 - 7(2x - 3)\) using the distributive property, we have already rewritten it as follows:

\[ 19 - 7(2x - 3) = 19 + -7(2x + -3) \]

Now, using the distributive property, we can further break it down:

\[ = 19 + (-7 \cdot 2x) + (-7 \cdot -3) \]

Now we perform the multiplications:

1. For \(-7 \cdot 2x\), we get \(-14x\).
2. For \(-7 \cdot -3\), we get \(21\).

Putting it all back together gives us:

\[ 19 + (-14x) + 21 \]

Now we can combine the constant terms \(19\) and \(21\):

\[ 19 + 21 = 40 \]

So the final equivalent expression is:

\[ 40 - 14x \]

In summary:

\[ 19 - 7(2x - 3) = 40 - 14x \]