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Chapter 6: Problem 12

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. A number decreased by the difference between eight and the number

Short Answer

Expert verified
The English phrase 'A number decreased by the difference between eight and the number' can be translated into the algebraic expression \(2x - 8\).

Step by step solution

01

Decipher the English Phrase

The given phrase is 'A number decreased by the difference between eight and the number'. The word 'decreased' suggests subtraction. The word 'difference' also suggests subtraction. So, first find the difference between eight and the number, which is denoted by \(x\). This simplifies to \(8 - x\).
02

Decrease the Number by the Difference

Next, decrease the number (again, represented by \(x\)) by the difference from the first step. This is written in algebraic form as \(x - (8 - x)\).
03

Simplify the Expression

Next, simplify the expression \(x - (8 - x)\) by distributing the negative sign inside the parenthetical expression. This is done by reversing the sign of each term, which results in the expression \(x - 8 + x\). Combine like terms to further simplify the expression to obtain the result, which is \(2x - 8\).

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Most popular questions from this chapter

Solve the equations using the quadratic formula. \(4 x^{2}=12 x-9\)

Solve the quadratic equations by factoring. \(x^{2}+9 x=-8\)

Use FOIL to find the products. \((x-5)(x+3)\)

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Use FOIL to find the products. \((2 x-9)(7 x-4)\)
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