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Chapter 6: Problem 16

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. The difference between the product of six and a number and negative two times the number

Short Answer

Expert verified
The simplified algebraic expression is \(8x\).

Step by step solution

01

Convert the English phrase into an algebraic expression

The product of six and a number can be written as \(6x\). Then, negative two times the number translates to \(-2x\). The difference between these two expressions gives us the algebraic expression \(6x - (-2x)\).
02

Simplify the algebraic expression

The double negative in the expression can be simplified to a plus sign, changing the expression to \(6x + 2x\).
03

Combine like terms

Combining the like terms, that is, terms that have the same variable part, gives \(8x\) which is the simplified form of the expression.

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Most popular questions from this chapter

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

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-14 x+45\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(8 x^{2}+33 x+4\)

Solve the quadratic equations by factoring. \(x^{2}+x-42=0\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. It's easy to factor \(x^{2}+x+1\) because of the relatively small numbers for the constant term and the coefficient of \(x\).
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