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 +
)
Nice!
Use the distributive property to write an equivalent expression.
15x − 11(5 − 7x)

= 15x + -11(5 + −7x)

= 15x + (
·
) + (
·
)
You got it!
Multiply within each set of parentheses to write another equivalent expression.
15x - 11(5 - 7x)

= 15x + -11(5 + −7x)

= 15x + (-11 · 5) + (-11 · −7x)

= 15x +
+

Answer 1

Let's go through the steps to simplify the expression \(15x - 11(5 - 7x)\).

1. Rewrite using addition: \[ 15x - 11(5 - 7x) = 15x + -11(5 + -7x) \]

2. Apply the distributive property: \[ 15x + (-11)(5) + (-11)(-7x) \]

3. Multiply within each set of parentheses:

   • For \(-11 \times 5\): \[ -11 \cdot 5 = -55 \]
   • For \(-11 \times -7x\): \[ -11 \cdot -7x = 77x \]

Putting it all together, we have: \[ 15x + (-55) + 77x \]

Thus, we get: \[ 15x - 55 + 77x \]

4. Combine like terms: Combine \(15x\) and \(77x\): \[ (15x + 77x) - 55 = 92x - 55 \]

So the final expression is: \[ 92x - 55 \]

To summarize:

• The expression \(15x - 11(5 - 7x)\) simplifies to \(92x - 55\).