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3.3 – Solving Equations - One Variable Suggestions for Solving Linear Equations: 1. If parentheses exist, used the distributive property to remove them. 2. Simplify each side of the equation by combining like-terms. 3. Get the variable of interest to one side of the equation and all remaining terms to the other side. 4. Use the appropriate properties to get the variable’s coefficient to be 1. 5. Check the solution by substituting it into the original equation.

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3.3 – Solving Equations – One Variable Solve: Check:

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3.3 – Solving Equations – One Variable Solve:

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3.3 – Solving Equations – One Variable Check:

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3.3 – Solving Equations – One Variable Solve: Check:

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3.3 – Solving Equations – One Variable Solve: Check:

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3.4 – Solving Equations/Problem Solving Translate the sentences and solve. Four times a number is twenty. The sum of a number and -5 yields thirty-two.

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3.4 – Solving Equations/Problem Solving Translate the sentences and solve. Fifteen subtracted from a number amounts to negative twenty-three. Five times the difference of a number and seven is equal to negative eight.

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3.4 – Solving Equations/Problem Solving Translate the sentences and solve. The quotient of triple a number and five gives one.

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3.4 – Solving Equations/Problem Solving Translate the sentences and solve. The sum of a number and two equals six added to three times the number.

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3.4 – Solving Equations/Problem Solving General Guidelines for Problem Solving 1. Understand the problem. Read the problem carefully. Construct a drawing if necessary. 2. Translate the information to an equation. 3. Solve the equation and check the solution. 4. Interpret the solution. Identify the unknown and select a variable.

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3.4 – Solving Equations/Problem Solving Write an equation and solve for the variable. The distance from Cincinnati, Ohio, to Denver, Colorado is 71 miles less than the distance from Denver to San Francisco, California. If the total of these two distances is 2399 miles, find the distance from Denver to San Francisco. Den. to SF: x Cin. to Den.: x - 71

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3.4 – Solving Equations/Problem Solving Write an equation and solve for the variable. A woman’s estate is valued at $57,000. According to her will, it is to be divided so her husband gets twice as much as her son. How much will each receive? son: x husband: 2x

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3.4 – Solving Equations/Problem Solving Write an equation and solve for the variable. Ray drives from his home to school and then to work. His total one-way driving distance is 100 miles. The drive to from school to work is twenty miles more than his drive from home to school. How long is each drive? home to school: x school to work: x + 20 miles

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3.4 – Solving Equations/Problem Solving Write an equation and solve for the variable. April spent $85 at a music store. She spent 4 times as much on CD’s than she did on a DVD. How much did she spend on the CD’s? CD:DVD:CD:DVD:

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Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

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