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Math  /  Algebra

QuestionWrite an.equivalent expression. 49−15⋅x\frac{4}{9}-\frac{1}{5} \cdot x
Choose the correct answer below. A. 49−15⋅x=−15x+49\frac{4}{9}-\frac{1}{5} \cdot x=-\frac{1}{5} x+\frac{4}{9} B. 49−15⋅x=−15(49−x)\frac{4}{9}-\frac{1}{5} \cdot x=-\frac{1}{5}\left(\frac{4}{9}-x\right) C. 49−15⋅x=x(49−15)\frac{4}{9}-\frac{1}{5} \cdot x=x\left(\frac{4}{9}-\frac{1}{5}\right) D. 49−15⋅x=15x−49\frac{4}{9}-\frac{1}{5} \cdot x=\frac{1}{5} x-\frac{4}{9}

Studdy Solution

STEP 1

What is this asking? Rewrite 49−15⋅x\frac{4}{9} - \frac{1}{5} \cdot x in a different way, without changing its value. Watch out! Don't get tricked by fancy factoring; we're just rearranging, not changing the expression's meaning!

STEP 2

1. Commute the terms

STEP 3

Our expression has two **terms**: 49\frac{4}{9} and −15⋅x- \frac{1}{5} \cdot x.
Remember, terms are separated by addition or subtraction.

STEP 4

The **commutative property of addition** says we can swap the order of terms being added without changing the sum.
We can rewrite our expression as: −15⋅x+49-\frac{1}{5} \cdot x + \frac{4}{9} Notice that we keep the sign with each term!

STEP 5

We can simplify −15⋅x- \frac{1}{5} \cdot x to −15x- \frac{1}{5}x.
So our final equivalent expression is: −15x+49-\frac{1}{5}x + \frac{4}{9}

STEP 6

The equivalent expression is −15x+49-\frac{1}{5}x + \frac{4}{9}, which matches answer choice **A**.

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