1. U SING T WO OR M ORE T RANSFORMATIONS Solving a Linear Equation Solve x + 6 = – 8 1313 To isolate the variable, undo the addition and then the multiplication. Write original equation. x = – 42 Simplify. Subtract 6 from each side. x + 6 – 6 = – 8 – 6 1313 Simplify. x = –14 1313 Multiply each side by 3. x ) = 3(–14) 1313 3(3( = – 8x + 6 1313 S OLUTION

2. 7x – 3x – 8 = 24 4x – 8 = 24 Combine like terms. 4x – 8 + 8 = 24 + 8 Add 8 to each side. 4x = 32 Divide each side by 4. x = 8 Solve 7x – 3x – 8 = 24. Combining Like Terms First 4x4x 4 = 32 4 Write original equation. Simplify. The solution is 8. When you check the solution, substitute 8 for each x in the original equation.

3. Using the Distributive Property Solve 5x + 3(x + 4) = 28. M ETHOD 1 Show All Steps M ETHOD 2 Do Some Steps Mentally 5x + 3(x + 4) = 28 5x + 3x + 12 = 28 8x + 12 = 28 8x + 12 – 12 = 28 – 12 8x = 16 x = 2 8x 16 88 = 5x + 3(x + 4) = 28 5x + 3x + 12 = 28 8x + 12 = 28 8x = 16 x = 2 M ETHOD 1 Show All Steps 5x + 3(x + 4) = 28 5x + 3x + 12 = 28 8x + 12 = 28 8x + 12 – 12 = 28 – 12 8x = 16 x = 2 8x 16 88 =

4. Solve 66 = (x + 3) 6565 – Write original equation. 66 = (x + 3) 6565 – –55 = x + 3 Simplify. Subtract 3 from each side. – 5 8 = x Multiplying by a Reciprocal First Solve 66 = (x + 3) 6565 – Multiply by reciprocal of. 6565 – It is easier to solve this equation if you don’t distribute first. 6565 – 66 = (x + 3) 5656 – 5656 – 6565 – Solving equations systematically is an example of deductive reasoning. Notice how each solution step is based on number properties or properties of equality.

5. S OLUTION Use the formula to convert 95 °F to Celsius. The Fahrenheit and Celsius scales are related by the equation F = C + 32 9595 A body temperature of 95 °F or lower may indicate the medical condition called hypothermia. What temperature on the Celsius scale may indicate hypothermia? S OLUTION Use the formula to convert 95 °F to Celsius. S OLVING R EAL- L IFE P ROBLEMS Using a Known Formula Write known formula. Substitute 95° for F. Subtract 32 from each side. Multiply by, the reciprocal of. 5959 9595 35 = C 95 = C + 32 9595 63 = C 9595 A temperature of 35°C or lower may indicate hypothermia. 9595 F = C + 32