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1.4 Rewrite Formulas and Equations Goal Your Notes p Rewrite and evaluate formulas and equations. VOCABULARY Formula Solve for a variable Literal equation Example 1 Rewrite a formula Solve the formula A 5 l p w for l. Then find the length of a rectangle with a width of 11 feet and an area of 187 square feet. Solution Step 1 Solve the formula for l. A5lpw 5l Write area formula. Divide both sides by . Step 2 Substitute the given value into the rewritten formula. l5 5 Substitute for w. Simplify. The length of the rectangle is 12 Lesson 1.4 • Algebra 2 Notetaking Guide for A and feet. Copyright © Holt McDougal. All rights reserved. 1.4 Rewrite Formulas and Equations Goal Your Notes p Rewrite and evaluate formulas and equations. VOCABULARY Formula An equation that relates two or more quantities, usually represented by variables Solve for a variable To rewrite a formula as an equivalent equation with a different variable alone on one side of the equation Literal equation An equation in which some or all of the coefficients and constants are indicated by letters Example 1 Rewrite a formula Solve the formula A 5 l p w for l. Then find the length of a rectangle with a width of 11 feet and an area of 187 square feet. Solution Step 1 Solve the formula for l. A5lpw A w } 5l Write area formula. Divide both sides by w . Step 2 Substitute the given value into the rewritten formula. 187 l5 } 11 5 17 Substitute 187 for A and 11 for w. Simplify. The length of the rectangle is 17 feet. 12 Lesson 1.4 • Algebra 2 Notetaking Guide Copyright © Holt McDougal. All rights reserved. Your Notes Checkpoint Complete the following exercises. 1. Solve the formula P 5 2l 1 2w for w. Then find the width of a rectangle with a length of 9 meters and a perimeter of 32 meters. 2. Solve the distance formula d 5 rt for t. Then find the time it takes to travel the distance of 135 miles at a rate of 30 miles per hour. Example 2 Solve a literal equation Solve the literal equation ax 1 b 5 c 1 d for x. Then use your general solution to solve the equation 2x 1 15 5 5 1 7. Solution Step 1 Solve ax 1 b 5 c 1 d for x. When you divide both sides of an equation by an unknown, remember to restrict the quantity to nonzero numbers to avoid dividing by 0. ax 1 b 5 c 1 d ax 5 c 1 d 2 Write original equation. Subtract x5 from each side. each side by . Step 2 Solve 2x 1 15 5 5 1 7 by substituting the given values into the rewritten formula. x5 Substitute for a, for b, for c, and for d. x5 Simplify. Checkpoint Complete the following exercise. 3. Solve the literal equation ax 2 b 5 c for x. Then use your general solution to solve the equation 4x 2 5 5 3. Copyright © Holt McDougal. All rights reserved. Lesson 1.4 • Algebra 2 Notetaking Guide 13 Your Notes Checkpoint Complete the following exercises. 1. Solve the formula P 5 2l 1 2w for w. Then find the width of a rectangle with a length of 9 meters and a perimeter of 32 meters. 7 meters 2. Solve the distance formula d 5 rt for t. Then find the time it takes to travel the distance of 135 miles at a rate of 30 miles per hour. 4.5 hours Solve a literal equation Example 2 Solve the literal equation ax 1 b 5 c 1 d for x. Then use your general solution to solve the equation 2x 1 15 5 5 1 7. Solution Step 1 Solve ax 1 b 5 c 1 d for x. When you divide both sides of an equation by an unknown, remember to restrict the quantity to nonzero numbers to avoid dividing by 0. ax 1 b 5 c 1 d ax 5 c 1 d 2 b c1d2b x5 } a Write original equation. Subtract b from each side. Divide each side by a . Step 2 Solve 2x 1 15 5 5 1 7 by substituting the given values into the rewritten formula. 5 1 7 2 15 x5 } 2 Substitute 2 for a, 15 for b, 5 for c, and 7 for d. x 5 2 1.5 Simplify. Checkpoint Complete the following exercise. 3. Solve the literal equation ax 2 b 5 c for x. Then use your general solution to solve the equation 4x 2 5 5 3. c1b x5} a ; x52 Copyright © Holt McDougal. All rights reserved. Lesson 1.4 • Algebra 2 Notetaking Guide 13 Your Notes Rewrite a linear equation Example 3 Solve 5x 2 4y 5 9 for y. Find y when x 5 23. Step 1 Solve the equation for y. 5x 2 4y 5 9 When dividing each side of an equation by the same number, remember to divide every term by the number. Write original equation. 24y 5 9 Subtract side. 1 y52 from each Divide each side by . Step 2 Substitute the given value into the equation. 1 y52 Substitute 23 for x. (23) y5 Example 4 Simplify. Rewrite a nonlinear equation Solve 8y 1 xy 5 10 for y. Find y when x 5 26. Step 1 Solve the equation for y. 8y 1 xy 5 10 y 5 10 10 y5 Write original equation. Distributive property Divide each side by . Step 2 Substitute the given value into the equation. 10 y5 5 Substitute 26 for x. Checkpoint Solve the equation for y. Then find the value of y when x 5 4. Homework 14 4. 2y 1 6x 5 14 Lesson 1.4 • Algebra 2 Notetaking Guide 5. 3y 2 4xy 5 26 Copyright © Holt McDougal. All rights reserved. Your Notes Example 3 Rewrite a linear equation Solve 5x 2 4y 5 9 for y. Find y when x 5 23. Step 1 Solve the equation for y. 5x 2 4y 5 9 When dividing each side of an equation by the same number, remember to divide every term by the number. Write original equation. 24y 5 9 2 5x Subtract 5x from each side. 9 5 1 } x y52 } 4 4 Divide each side by 24 . Step 2 Substitute the given value into the equation. 9 5 1 } (23) y52 } Substitute 23 for x. y 5 26 Simplify. 4 Example 4 4 Rewrite a nonlinear equation Solve 8y 1 xy 5 10 for y. Find y when x 5 26. Step 1 Solve the equation for y. 8y 1 xy 5 10 (8 1 x) y 5 10 10 y5 81x Write original equation. Distributive property Divide each side by 81x . Step 2 Substitute the given value into the equation. 10 y5 5 5 Substitute 26 for x. 8 1 (26) Checkpoint Solve the equation for y. Then find the value of y when x 5 4. Homework 4. 2y 1 6x 5 14 y 5 7 2 3x; 25 14 Lesson 1.4 • Algebra 2 Notetaking Guide 5. 3y 2 4xy 5 26 26 y5} ; 22 3 2 4x Copyright © Holt McDougal. All rights reserved.