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Chapter 6: Problem 17

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. The difference between eight times a number and six more than three times the number

Short Answer

Expert verified
The algebraic expression for the given English phrase is \(5x-6\)

Step by step solution

01

Translation into Algebraic Expression

First, translate each part of the phrase into an algebraic expression. The phrase 'eight times a number' can be written as \(8x\). The phrase 'six more than three times the number' can be written as \(3x+6\). So the whole phrase 'The difference between eight times a number and six more than three times the number' can be expressed as the algebraic expression \(8x - (3x + 6)\).
02

Simplify the Expression

Now, simplify the expression by distributing the subtraction across the terms in the bracket. Remember that subtracting a positive number is equivalent to adding a negative number. So, the equation becomes \(8x - 3x - 6\). Further simplifying by combining like terms, we get \(5x-6\) .

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Most popular questions from this chapter

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-9 x-36\)

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Solve the equations using the quadratic formula. \(x^{2}+6 x-10=0\)

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