Math  /  Algebra

QuestionWhich uses the GCF to generate an expression equivalent to 8323x\frac{8}{3}-\frac{2}{3} x ? 13(43x)\frac{1}{3}(4-3 x) 13(x4)\frac{1}{3}(x-4) 23(4x)\frac{2}{3}(4-x) 23(x4)\frac{2}{3}(x-4)

Studdy Solution

STEP 1

1. The expression given is 8323x\frac{8}{3} - \frac{2}{3}x.
2. We are looking for an equivalent expression using the greatest common factor (GCF).
3. The GCF of the terms in the expression is the largest factor that divides each term.

STEP 2

1. Identify the terms in the expression.
2. Determine the GCF of the terms.
3. Factor out the GCF from the expression.
4. Compare the factored expression to the given options.

STEP 3

Identify the terms in the expression 8323x\frac{8}{3} - \frac{2}{3}x.
The terms are 83\frac{8}{3} and 23x-\frac{2}{3}x.

STEP 4

Determine the GCF of the terms 83\frac{8}{3} and 23x-\frac{2}{3}x.
The GCF of 83\frac{8}{3} and 23x-\frac{2}{3}x is 23\frac{2}{3}.

STEP 5

Factor out the GCF 23\frac{2}{3} from the expression 8323x\frac{8}{3} - \frac{2}{3}x.
8323x=23(4)23(x)=23(4x)\frac{8}{3} - \frac{2}{3}x = \frac{2}{3}(4) - \frac{2}{3}(x) = \frac{2}{3}(4 - x)

STEP 6

Compare the factored expression 23(4x)\frac{2}{3}(4 - x) to the given options:
- 13(43x)\frac{1}{3}(4-3x) - 13(x4)\frac{1}{3}(x-4) - 23(4x)\frac{2}{3}(4-x) - 23(x4)\frac{2}{3}(x-4)
The equivalent expression is 23(4x)\frac{2}{3}(4-x).
The expression equivalent to 8323x\frac{8}{3} - \frac{2}{3}x using the GCF is 23(4x)\boxed{\frac{2}{3}(4-x)}.

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