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Chapter 1: Problem 79

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

Short Answer

Expert verified
The general approach to solving algebraic word problems involves understanding the problem, defining the unknowns, setting up the equations, solving these equations and finally, verifying the solutions.

Step by step solution

01

Understanding the Problem

The first step involves reading the problem carefully and identifying what the problem is asking for. This step is crucial in figuring out the unknowns, which will be represented as variables in the algebraic equations.
02

Defining the Unknowns

After understanding the problem, assign a variable to represent the quantity that we are trying to find. If there are several unknowns, assign a separate variable for each.
03

Setting Up the Equations

Using the problem's information, set up an equation that describes the relationships between the different unknowns. Every clue in the problem should be incorporated into the equation.
04

Solving the Equations

Solve the equation(s) to find the value of the variables. This could involve methods such as addition, subtraction, multiplication, division, factoring or use of quadratic formula, depending upon the nature of the equations.
05

Verifying the Solutions

The last step is verification. To ensure the obtained solutions make sense in the context of the original problem, substitute the solution back into the original equation to see if it is satisfied.

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Most popular questions from this chapter

In Exercises \(73-74\), use the method for solving quadratic inequalities to solve each higher-order polynomial inequality. $$ x^{3}+2 x^{2}-x-2 \geq 0 $$

In Exercises \(1-8,\) add or subtract as indicated and write the result in standard form. $$7-(-9+2 i)-(-17-6 i)$$

In Exercises \(54-56,\) perform the indicated operations and write the result in standard form. \((8+9 i)(2-i)-(1-i)(1+i)\)

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$(3 \sqrt{-5})(-4 \sqrt{-12})$$

Which one of the following is true? a. The solution set of \(x^{2}>25\) is \((5, \infty)\) b. The inequality \(\frac{x-2}{x+3}<2\) can be solved by multiplying both sides by \(x+3\), resulting in the equivalent inequality \(x-2<2(x+3)\) c. \((x+3)(x-1) \geq 0\) and \(\frac{x+3}{x-1} \geq 0\) have the same solution set. d. None of these statements is true.
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