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**Warm-Up #2 Simplify the expression. 2. –6(m – 9) + 14m – 20**

1. 8b – 3(4 – b) ANSWER 11b – 12 ANSWER 8m + 34 3. You bought a pair of jeans for n dollars in a city where the sales tax rate is 5%. Write an expression for the total cost of the jeans, including sales tax. ANSWER n n, or 1.05n

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**Solve an equation with a variable on one side**

EXAMPLE 1 Solve an equation with a variable on one side Solve 4 5 x + 8 = 20. 4 5 x + 8 = 20 Write original equation. 4 5 x = 12 Subtract 8 from each side. x = (12) 5 4 Multiply each side by , the reciprocal of 5 4 x = 15 Simplify. ANSWER The solution is 15. CHECK x = 15 in the original equation. 4 5 x + 8 = (15) + 8 = = 20

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EXAMPLE 2 Write and use a linear equation During one shift, a waiter earns wages of $30 and gets an additional 15% in tips on customers’ food bills. The waiter earns $105. What is the total of the customers’ food bills? Restaurant SOLUTION Write a verbal model. Then write an equation. Write 15% as a decimal.

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**Write and use a linear equation**

EXAMPLE 2 Write and use a linear equation 105 = x Write equation. 75 = 0.15x Subtract 30 from each side. 500 = x Divide each side by 0.15. The total of the customers’ food bills is $500. ANSWER

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GUIDED PRACTICE for Examples 1 and 2 Solve the equation. Check your solution. x + 9 = 21 ANSWER The solution is x = 3. x – 41 = – 13 ANSWER The solution is x = 4. 3. 3 5 – x + 1 = 4 ANSWER The solution is -5.

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**Solve an equation using the distributive property**

EXAMPLE 4 Solve an equation using the distributive property Solve 3(5x – 8) = –2(–x + 7) – 12x. 3(5x – 8) = –2(–x + 7) – 12x Write original equation. 15x – 24 = 2x – 14 – 12x Distributive property 15x – 24 = – 10x – 14 Combine like terms. 25x – 24 = –14 Add 10x to each side. 25x = 10 Add 24 to each side. x = 2 5 Divide each side by 25 and simplify. ANSWER The solution 2 5

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**Solve an equation using the distributive property**

EXAMPLE 4 Solve an equation using the distributive property CHECK 2 5 3( – 8) –2(– ) – 12 = ? 2 5 Substitute for x. 3(–6) –14 – 4 5 = ? 24 Simplify. – 18 = – 18 Solution checks.

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GUIDED PRACTICE for Examples 3, 4, and 5 Solve the equation. Check your solution. 5. –2x + 9 = 2x – 7 ANSWER The correct answer is 4. – x = –6x + 15 ANSWER The correct answer is 1. (x + 2) = 5(x + 4) ANSWER The solution is –7.

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GUIDED PRACTICE for Examples 3, 4, and 5 Solve the equation. Check your solution. 8. –4(2x + 5) = 2(–x – 9) – 4x ANSWER The solution x = – 1 x x = 39 1 4 2 5 9. ANSWER The correct answer is 60

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**Rewrite a formula with two variables**

EXAMPLE 1 Rewrite a formula with two variables Solve the formula C = 2πr for r. Then find the radius of a circle with a circumference of 44 inches. SOLUTION STEP 1 Solve the formula for r. C = 2πr Write circumference formula. C 2π = r Divide each side by 2π. STEP 2 Substitute the given value into the rewritten formula. r = C 2π = 44 7 Substitute 44 for C and simplify. The radius of the circle is about 7 inches. ANSWER

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GUIDED PRACTICE for Example 1 The formula for the distance d between opposite vertices of a regular hexagon is d = where a is the distance between opposite sides. Solve the formula for a. Then find a when d = 10 centimeters. 2. 2a 3 SOLUTION d 3 a = 2 3 5 When d = 10cm, a = or cm

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**Rewrite a formula with three variables**

EXAMPLE 2 Rewrite a formula with three variables Solve the formula P = 2l + 2w for w. Then find the width of a rectangle with a length of 12 meters and a perimeter of 41 meters. SOLUTION Solve the formula for w. STEP 1 P = 2l + 2w Write perimeter formula. P – 2l = 2w Subtract 2l from each side. P – 2l 2 = w Divide each side by 2.

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**Rewrite a formula with three variables**

EXAMPLE 2 Rewrite a formula with three variables Substitute the given values into the rewritten formula. STEP 2 41 – 2(12) 2 w = Substitute 41 for P and 12 for l. w = 8.5 Simplify. The width of the rectangle is 8.5 meters. ANSWER

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GUIDED PRACTICE for Example 2 Solve the formula P = 2l + 2w for l. Then find the length of a rectangle with a width of 7 inches and a perimeter of 30 inches. 3. Length of rectangle is 8 in. ANSWER Solve the formula A = lw for w. Then find the width of a rectangle with a length of 16 meters and an area of 40 square meters. 4. Write of rectangle is 2.5 m w = A l ANSWER

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GUIDED PRACTICE for Example 2 Solve the formula for the variable in red. Then use the given information to find the value of the variable. A = 1 2 bh 5. Find h if b = 12 m and A = 84 m2. ANSWER = h 2A b

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GUIDED PRACTICE for Example 2 Solve the formula for the variable in red. Then use the given information to find the value of the variable. A = 1 2 bh 6. and A = 9 cm2. Find b if h = 3 cm ANSWER = b 2A h

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GUIDED PRACTICE for Example 2 Solve the formula for the variable in red. Then use the given information to find the value of the variable. A = 1 2 7. (b1 + b2)h Find h if b1 = 6 in., b2 = 8 in., and A = 70 in.2 ANSWER h = 2A (b1 + b2)

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**Rewrite a linear equation**

EXAMPLE 3 Rewrite a linear equation Solve 9x – 4y = 7 for y. SOLUTION Solve the equation for y. STEP 1 9x – 4y = 7 Write original equation. –4y = 7 – 9x Subtract 9x from each side. y = 9 4 7 – + x Divide each side by –4.

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**Rewrite a nonlinear equation**

EXAMPLE 4 Rewrite a nonlinear equation Solve 2y + xy = 6 for y. SOLUTION Solve the equation for y. STEP 1 2y + x y = 6 Write original equation. (2+ x) y = 6 Distributive property y = 6 2 + x Divide each side by (2 + x).

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GUIDED PRACTICE for Examples 3 and 4 Solve the equation for y. Then find the value of y when x = 2. 8. y – 6x = 7 9. 5y – x = 13 10. 3x + 2y = 12 y = x y = 19 ANSWER y = x 5 13 + y = 3 ANSWER y = – 3x 2 + 6 ANSWER y = 3

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GUIDED PRACTICE for Examples 3 and 4 Solve the equation for y. Then find the value of y when x = 2. 11. 2x + 5y = –1 12. 3 = 2xy – x 13. 4y – xy = 28 2x 5 –1 – y = –1 y = ANSWER y = 1 4 3 +x 2x ANSWER y = 14 28 4 – x y = ANSWER

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CLASSWORK Workbook 1-3 (1-25 odd) Workbook 1-4 (1-25 odd)

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