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Chapter 6: Problem 15

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

Short Answer

Expert verified
The English phrase translates into the algebraic expression \(5x - 2x\) which simplifies to \(3x\).

Step by step solution

01

Conversion into Mathematical Expression

The English phrase can be decoded as follows: 'The difference between the product of five and a number' can be expressed as 5*x. 'Twice the number' can be written as 2*x. The entire phrase is asking for the difference between these two quantities, which can be represented as \(5x - 2x\).
02

Simplifying the Algebraic Expression

The two terms in the algebraic expression \(5x - 2x\) are like terms as they have the same variable of the same power. They can be combined. Continue with the subtraction \(5x 鈥� 2x\) which simplifies to \(3x\).

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Most popular questions from this chapter

When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.

Solve the quadratic equations by factoring. \(3 x^{2}-4 x=15\)

When the sum of 6 and twice a positive number is subtracted from the square of the number, 0 results. Find the number.

Explain how to multiply two binomials using the FOIL method. Give an example with your explanation.

Solve the equations using the quadratic formula. \(x^{2}+4 x=6\)
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