11-3. IWBAT solve equations with variables on both sides of the equal sign.
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1 IWBAT solve equations with variables on both sides of the equal sign.
2 WRITE: Some problems produce equations that have variables on both sides of the equal sign. Solving an equation with variables on both sides is similar to solving an equation with a variable on only one side. You can add or subtract a term containing a variable on both sides of an equation.
3 EX 1A: Variables on Both Sides Solve. 4x + 6 = x 4x + 6 = x 4x 4x 6 = 3x 6 3x 3 = 3 2 = x Subtract 4x from both sides. Divide both sides by 3.
4 WRITE: Helpful Hint Check your solution by substituting the value back into the original equation. For example, 4(-2) + 6 = -2 or -2 = -2.
5 EX 1B: Variables on Both Sides Solve. 9b 6 = 5b b 6 = 5b b 5b 4b 6 = b = 24 4b 24 4 = 4 b = 6 Subtract 5b from both sides. Add 6 to both sides. Divide both sides by 4.
6 EX 1C: Variables on Both Sides Solve. 9w + 3 = 9w + 7 9w + 3 = 9w + 7 9w 9w Subtract 9w from both sides. 3 7 No solution. There is no number that can be substituted for the variable w to make the equation true.
7 WRITE: Helpful Hint If the variables in an equation are eliminated and the resulting statement is false, the equation has no solution.
8 WRITE: To solve multi-step equations with variables on both sides, first combine like terms and clear fractions. Then add or subtract variable terms to both sides so that the variable occurs on only one side of the equation. Then use properties of equality to isolate the variable.
9 EX 2: Solving Multi-Step Equations with Variables on Both Sides Solve. 10z 15 4z = 8 2z z 15 4z = 8 2z 15 6z 15 = 2z 7 Combine like terms. + 2z + 2z Add 2z to both sides. 8z 15 = z = 8 8z = z = 1 Add 15 to both sides. Divide both sides by 8.
10 EX 3: Business Application Daisy s Flowers sell a rose bouquet for $39.95 plus $2.95 for every rose. A competing florist sells a similar bouquet for $26.00 plus $4.50 for every rose. Find the number of roses that would make both florists bouquets cost the same price.
11 EX 3 Continued r = r Let r represent the price of one rose. 2.95r 2.95r = r Subtract 2.95r from both sides Subtract from both sides = 1.55r r = Divide both sides by = r The two services would cost the same when purchasing 9 roses.
12 EX 4: Multi-Step Application Jamie spends the same amount of money each morning. On Sunday, he bought a newspaper for $1.25 and also bought two doughnuts. On Monday, he bought a newspaper for fifty cents and bought five doughnuts. On Tuesday, he spent the same amount of money and bought just doughnuts. How many doughnuts did he buy on Tuesday?
13 EX 4 Continued First solve for the price of one doughnut. Let d represent the price d = d of one doughnut. 2d 2d 1.25 = d = 3d = d Subtract 2d from both sides. Subtract 0.50 from both sides. = 3d Divide both sides by 3. 3 The price of one doughnut is $0.25.
14 EX 4 Continued Now find the amount of money Jamie spends each morning d Choose one of the original expressions (0.25) = n 0.25 = Jamie spends $1.75 each morning. Find the number of doughnuts Jamie buys on Tuesday. 0.25n = 1.75 Let n represent the number of doughnuts. Divide both sides by n = 7; Jamie bought 7 doughnuts on Tuesday.
15 EX 5: Solving Literal Equations for a Variable The equation t = m + 10e gives the test score t for a student who answers m multiple-choice questions and e essay questions correctly. Solve this equation for e. t = m + 10e Locate e in the equation. t = m + 10e m m t m = t m = 10e t m = e 10 10e Since m is added to 10e, subtract m from both sides. Since e is multiplied 10, divide both sides by 10.
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![Can I take positive 5 from both sides of the equation? [Yes]](/thumbs/89/99813942.jpg "Can I take positive 5 from both sides of the equation? [Yes]")
Eample # Solve 5 +. 5 + 5+ 5+ 5 + 5 + Choral Response Five plus a number is. How can we get a five on both sides of the equation? [Decompose, 5+] Now can we take a positive 5 from both sides? [Yes] What