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Simplifying Expressions and Solving Equation Word Problems Study Guide (page 3)

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Updated on Oct 3, 2011

Equation Word Problems

Now that the steps to solving equations have been practiced, let's apply these steps to solving word problems involving equations. Use the chart at the beginning of the lesson and the examples in Lesson 1 for help with translating phrases into math symbols and equations. Then, use your knowledge and skills in equation solving to find the correct solution to each problem. In addition, use the word-problem solving steps to be sure each detail is taken care of and all problems are checked.

Tip:

To check solutions in equations, substitute the value into the original equation and use order of operations. The correct order of operations is Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. It is commonly remembered as the acronym PEMDAS.

Example 1

Ten more than a number is equal to 40. What is the number?

Read and understand the question. This question is looking for a number when clues about this number are given.

Make a plan. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

Carry out the plan. Let x = a number. The key phrase more than means addition. The statement translates to x + 10 = 40. Next, subtract 10 from each side of the equation to get the variable alone.

    x + 10 – 10 = 40 – 10
    x = 30

Check your answer. Check your solution by substituting the answer into the equation.

    x + 10 = 40

becomes

    30 + 10 = 40
    40 = 40

This answer is checking.

Example 2

Eight less than twice a number is equal to four times the number. What is the number?

Read and understand the question. This question is looking for a number when clues about this number are given.

Make a plan. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

Carry out the plan. Let x = a number. The key phrase less than means subtraction and twice a number is written as 2x. The first part of the statement translates to 2x – 8. In the second part of the sentence, four times the number is written as 4x. The entire equation is

    2x – 8 = 4x

Get the variables on one side of the equation by subtracting 2x from each side.

    2x – 2x – 8 = 4x – 2x

The equation simplifies to

    –8 = 2x

Next, divide each side by 2 to get the variable alone.

    x = –4.

Check your answer. Check your solution by substituting the answer into the equation.

    2x – 8 = 4x

becomes

      2(–4) – 8 = 4(–4)
      –8 – 8 = –16
      –16 = –16

This answer is checking.

Example 3

Forty-two added to a number is equal to 6 times the sum of the number and 2. What is the number?

Read and understand the question. This question is looking for a number when clues about this number are given.

Make a plan. Translate the statement into equation form. Then, solve the equation using the equation solving steps.

Carry out the plan. Let x = a number. The key phrase added to means addition. The first part of the statement translates to x + 42. The second part of the sentence, six times the sum of a number and 2 is written as 6(x + 2). The entire equation is

    x + 42 = 6(x + 2)

Use the distributive property on the right side to make the equation

    x + 42 = 6x + 12

Get the variables on one side of the equation by subtracting x from each side.

    xx + 42 = 6xx + 12

The equation simplifies to

    42 = 5x + 12

Subtract 12 from each side of the equation to get 30 = 5x. Next, divide each side by 5 to get the variable alone:

    x = 6

Check your answer. Check your solution by substituting the answer into the equation.

    x + 42 = 6(x + 2)

becomes

      6 + 42 = 6(6 + 2)
      48 = 6(8)
      48 = 48

This answer is checking.

Find practice problems and solutions for these concepts at Simplifying Expressions and Solving Equation Word Problems Practice Questions.

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