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Chapter 0: Problem 57

In your own words, describe a step-by-step approach for solving algebraic word problems.

Short Answer

Expert verified
Understanding the given information and translating it into an algebraic expression is crucial. After this, algebraic principles are used to solve the equations and the answer is then interpreted in the context of the problem. The solution should always be checked to ensure its correctness.

Step by step solution

01

Understand the problem

Read the problem carefully, note key details about the variables (the unknowns), their relationships, and the information you are asked to find.
02

Translate the words into algebra

Take each piece of information given in the problem and express it in terms of algebraic expressions or equations. This translates the real world problem into a mathematical problem.
03

Solving the equations

Use the principles of algebra to simplify and solve the equations. Follow the order of operations to solve equations correctly.
04

Check the solution

Check your answer by substituting your solution back into the original problem.
05

Interpret the results

Translate the mathematical solution back into the context of the original problem. This is important to ensure the solution makes sense in context and answers the question posed.

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Most popular questions from this chapter

Exercises \(159-161\) will help you prepare for the material covered in the next section. In parts (a) and (b), complete each statement. a. \(\frac{b^{7}}{b^{3}}=\frac{b \cdot b \cdot b \cdot b \cdot b \cdot b \cdot b}{b \cdot b \cdot b}=b^{2}\) b. \(\frac{b^{8}}{b^{2}}=\frac{b \cdot b \cdot b \cdot b \cdot b \cdot b \cdot b \cdot b}{b \cdot b}=b^{?}\) c. Generalizing from parts (a) and (b), what should be done with the exponents when dividing exponential expressions with the same base?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$534.7=5.347 \times 10^{3}$$

Will help you prepare for the material covered in the next section. A telephone texting plan has a monthly fee of 20 dollar with a charge of 0.05 dollar per text. Write an algebraic expression that models the plan's monthly cost for \(x\) text messages.

Will help you prepare for the material covered in the next section. Jane's salary exceeds Jim's by 150 dollar per week. If \(x\) represents Jim's weekly salary, write an algebraic expression that models Jane's weekly salary.

Explain how to determine the restrictions on the variable for the equation $$\frac{3}{x+5}+\frac{4}{x-2}=\frac{7}{x^{2}+3 x-6}$$
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