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

Question

Use the distributive property to write equivalent expressions.
Rewriting subtraction using addition can be helpful to keep track of the subtraction symbol when distributing. Start by rewriting this expression using addition.
15x − 11(5 − 7x)

= 15x +
(5 +
)

Answer 1

To rewrite the expression \( 15x - 11(5 - 7x) \) using addition, we can first change the subtraction into addition by rewriting it as follows:

\[ 15x - 11(5 - 7x) = 15x + (-11)(5 - 7x) \]

Next, we can distribute the \(-11\) inside the parentheses:

\[ (-11)(5 - 7x) = -11 \cdot 5 + (-11)(-7x) = -55 + 77x \]

Now we can substitute this back into the expression:

\[ 15x + (-55 + 77x) \]

Which can be simplified further:

\[ 15x + (-55) + 77x \]

Thus, the expression \( 15x - 11(5 - 7x) \) can be rewritten as:

\[ 15x + (-55 + 77x) \]

Now we can combine like terms if needed.

So, the final expression after rewriting using addition is:

\[ 15x + (-55 + 77x) = (15x + 77x) + (-55) = 92x - 55 \]

Therefore, the answer is:

\[ 15x + (-55) + 77x \]

Where \( 15x \) and \( 77x \) are like terms.