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This month you have a total of \( \$ 6000 \) in interest-bearing credit card debt, split between a card charging \( 15 \% \) annual interest and a card charging \( 24 \% \) annual interest. If the interest-bearing balance on the card charging \( 15 \% \) is \( x \) dollars, then the total interest for the month is given by the following algebraic expression. Complete parts a through c below. \( 0.0125 x+0.02(6000-x) \) a. Simplify the algebraic expression. \( 0.0125 x+0.02(6000-x)=\square \)

Ask by Phillips Griffin. in the United States
Jan 29,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The simplified algebraic expression is \( -0.0075x + 120 \).

Solution

Calculate or simplify the expression \( 0.0125x+0.02(6000-x) \). Simplify the expression by following steps: - step0: Solution: \(0.0125x+0.02\left(6000-x\right)\) - step1: Expand the expression: \(0.0125x+120-0.02x\) - step2: Subtract the terms: \(-0.0075x+120\) The simplified algebraic expression is \( -0.0075x + 120 \).

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The Deep Dive

To simplify the algebraic expression \( 0.0125 x + 0.02(6000 - x) \), first distribute the \( 0.02 \) across the \( (6000 - x) \): \[ 0.0125 x + 0.02 \cdot 6000 - 0.02 \cdot x \] This becomes: \[ 0.0125 x + 120 - 0.02 x \] Now, combine the terms involving \( x \): \[ (0.0125 - 0.02)x + 120 = -0.0075 x + 120 \] So, the simplified expression is: \[ -0.0075 x + 120 \]

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