IntroductionLiteral equations are equations that involve two or more variables. Sometimes it is useful to rearrange or solve literal equations for a specific variable in order to find a solution to a given problem. In this lesson, literal equations and formulas, or literal equations that state specific rules or relationships among quantities, will be examined.

1.5.1: Rearranging Formulas

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Key Concepts• It is important to remember that both literal equations

and formulas contain an equal sign indicating that both sides of the equation must remain equal.

• Literal equations and formulas can be solved for a specific variable by isolating that variable.

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Key Concepts, continued

• To isolate the specified variable, use inverse

operations. When coefficients are fractions, multiply

both sides of the equation by the reciprocal. The

reciprocal of a number, also known as the inverse of

a number, can be found by flipping a number.

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Key Concepts, continued

• Think of an integer as a fraction with a denominator of 1.

To find the reciprocal of the number, flip the fraction.

The number 2 can be thought of as the fraction .

To find the reciprocal, flip the fraction: becomes .

You can check if you have the correct reciprocal

because the product of a number and its reciprocal is

always 1.

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Common Errors/Misconceptions• solving for the wrong variable

• improperly isolating the specified variable by using the opposite inverse operation

• incorrectly simplifying terms

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1.5.1: Rearranging Formulas

Guided Practice

Example 3Solve 4y + 3x = 16 for y.

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Guided Practice: Example 3, continued

1. Begin isolating y by subtracting 3x from both sides of the equation.

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Guided Practice: Example 3, continued

2. To further isolate y, divide both sides of the equation by the coefficient of y. The coefficient of y is 4. Be sure that each term of the equation is divided by 4.

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1.5.1: Rearranging Formulas

Guided Practice: Example 3, continued

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Guided Practice

Example 4

The formula for finding the area of a triangle is ,

where b is the length of the base and h is the height of

the triangle. Suppose you know the area and height of

the triangle, but need to find the length of the base. In

this case, solving the formula for b would be helpful.

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Guided Practice: Example 4, continued

1. Begin isolating b by multiplying both

sides of the equation by the reciprocal of

, or 2.

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Guided Practice: Example 4, continued

Multiplying both sides of the equation by the

reciprocal is the same as dividing both sides of the

equation by . The result will be the same.

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Guided Practice: Example 4, continued

2. To further isolate b, divide both sides of the equation by h.

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or

Guided Practice: Example 4, continued

3. The formula for finding the length of the base of a triangle can be found by doubling the area and dividing the result by the height of the triangle.

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1.5.1: Rearranging Formulas

Guided Practice: Example 4, continued

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