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# 7.1 Solving Two Step Equations

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Chapter 7, Section 1: Solving Two-Step Equations.

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### 7.1 Solving Two Step Equations

1. 1. Chapter 7 Solving Equations and Inequalities Section 1: Solving Two-Step Equations January 5 th , 2009 Last Chapter of Quarter 2
2. 2. Spray On Warm Up! Distributive Property <ul><li>(-5)(4x – 3) </li></ul><ul><li>(7)(2x + 5) </li></ul><ul><li>(3)(6m + 1) </li></ul>
3. 3. Solving Two-Step equations <ul><li>There is a model method, but who cares about that. </li></ul><ul><li>To SOLVE, find the value of a variable, a two-step equation, first undo addition or subtraction, then undo multiplication and division. </li></ul>In other words, to SOLVE, do PEMDAS backwards. (SADMEP)
4. 4. Check Your Work <ul><li>3n – 6 = 15 </li></ul><ul><li>+ 6 + 6 </li></ul><ul><li>3n = 21 </li></ul><ul><li>3 3 </li></ul><ul><li>n = 7 </li></ul><ul><li>Equation </li></ul><ul><li>Addition Prop. of Equality </li></ul><ul><li>Simplify </li></ul><ul><li>Division Prop. of Equality </li></ul><ul><li>Solve </li></ul>Now that we know n = 7, to check, we stick it back in to check.
5. 5. Check Your Work <ul><li>3( 7 ) – 6 = 15 </li></ul><ul><li>21 - 6 = 15 </li></ul><ul><li>15 = 15 </li></ul><ul><li>Equation with variable. </li></ul><ul><li>Simplify </li></ul><ul><li>Solve, true statement. </li></ul>Now that we know n = 7, to check, we stick it back in to check.
6. 6. Solve and Check Your Solution <ul><li>15x + 3 = 48 </li></ul><ul><li>T/4 – 10 = -6 </li></ul><ul><li>9g + 11 = 2 </li></ul>
7. 7. The Dietary Soccer Player <ul><li>A soccer player wants to eat 700 calories at a meal that includes a Reuben sandwich and pickles. The sandwich has 464 calories, and the pickles have 7 calories each. </li></ul><ul><li>Solve the equation 464 + 7f = 700 to find the number of pickles the soccer player can eat. </li></ul>
8. 8. The Dietary Soccer Player <ul><li>A soccer player wants to eat 700 calories at a meal that includes a Reuben sandwich and pickles. The sandwich has 464 calories, and the pickles have 7 calories each. </li></ul><ul><li>Suppose the soccer player drinks a 200 calorie sports drink with the meal. Create another equation that incorporates the drink to determine how many pickles the soccer player can now eat to stay within his diet. </li></ul>
9. 9. Solve and Check Your Solution <ul><li>15x + 3 = 48 </li></ul><ul><li>T/4 – 10 = -6 </li></ul><ul><li>9g + 11 = 2 </li></ul>
10. 10. Reminder About Equations and Negative Variables <ul><li>What is –x? </li></ul><ul><li>-x is like saying (-1)x or –1 • x. </li></ul><ul><li>Therefore, -x is the opposite of x. </li></ul><ul><li>Solve: 5 – x = 17 </li></ul><ul><li>+ (-5) + (-5) </li></ul><ul><li>0 - x = 12 </li></ul><ul><li>(-1) (-1) </li></ul><ul><li>x = -12 </li></ul>Equation Addition Prop. of Equality Simplify Division Prop. of Equality Solution Now Check Your Answer!
11. 11. Try These <ul><li>-a + 6 = 8 </li></ul><ul><li>-9 – (y/7) = -12 </li></ul><ul><li>13 – 6f = 31 </li></ul>
12. 12. Two Step Equations in Real Life <ul><li>Lynne saves \$45 each week. She now has \$180. She plans to save for a trip to Puerto Rico. To find how many weeks w she will take to save \$900, </li></ul><ul><li>solve \$180 + \$45w = \$900. </li></ul>It will take Lynne 16 weeks from now, to save up 900 bucks.
13. 13. Try This One <ul><li>Jacob bought four begonias in 6 inch pots and a \$19 fern at a fund-raiser. He spent a total of \$83. Solve the equation 4p + \$19 = \$83 to find the price p of each begonia. </li></ul>Each pot of begonias cost \$16.
14. 14. Assignment #52: <ul><li>Page 338: 1-31 All. </li></ul>