### About Translating Phrases to Expressions:

Many students struggle when it comes to solving word problems. In order to really understand how to set up and solve a word problem, our first task is to be able to translate between a given phrase and the corresponding algebraic expression.

Test Objectives

- Demonstrate the ability to translate between a given phrase and an algebraic expression
- Demonstrate the ability to solve a basic word problem with linear equations

#1:

Instructions: solve each word problem.

a) If the difference of a number and 1 is multiplied by 2, the result is the same as 3 less than 5 times the number. Find the number.

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#2:

Instructions: solve each word problem.

a) If 2 is added to 5 times a number, the result is the same as 5 more than 4 times the number. Find the number.

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#3:

Instructions: solve each word problem.

a) If the difference of 3 times a number and 7 is multiplied by 5, the result is the same as 5 less than 6 multiplied by the difference of the number and 2. Find the number.

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#4:

Instructions: solve each word problem.

a) The quotient of a number and 9 is the same as 2 times the difference of the number and 1. Find the number.

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#5:

Instructions: solve each word problem.

a) If the quotient of a number and 5 is added to 3, the result is the same as 12/5 being subtracted away from 2 times the sum of the number and 9. Find the number.

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}\frac{1}{3}$$

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#2:

Solutions:

$$a)\hspace{.2em}3$$

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#3:

Solutions:

$$a)\hspace{.2em}2$$

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#4:

Solutions:

$$a)\hspace{.2em}\frac{18}{17}$$

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#5:

Solutions:

$$a)\hspace{.2em}-7$$