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Chapter 6: Problem 13

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. Six times the product of negative five and a number

Short Answer

Expert verified
The algebraic expression for the English phrase 'six times the product of negative five and a number' is \(-30x\).

Step by step solution

01

Translate English Phrase into Algebraic Expression

From the given English phrase, we construct the algebraic expression as follows: 'six times the product of negative five and a number' can be written as '6 times (-5 times x)'. In algebraic expression format, it becomes \(6 \times (-5 \times x)\) or simply \(6(-5x)\).
02

Simplify the Algebraic Expression

Now, we simplify this algebraic expression by carrying out the multiplication operation. The multiplication operation is commutative, so we can multiply the coefficients in any order. Thus, for \(6(-5x)\), the simplification results in: \(-30x\).

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I began the solution of \(5-3(x+2)>10 x\) by simplifying the left side, obtaining \(2 x+4>10 x\).

Solve each equation by the method of your choice. \((2 x-6)(x+2)=5(x-1)-12\)

Factor the trinomials in Exercises 9-32, or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}+5 x+6\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(2 x^{2}+7 x+3\)

Solve the quadratic equations by factoring. \(x^{2}-14 x=-49\)
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