3Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsProblem of the DayRay and Katrina are wandering through the wildlife preserve. They observe and count a total of 15 wild turkeys and deer and a total of 46 legs. How many of each did they see?7 turkeys, 8 deer
4Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsLearn to combine like terms in an expression.
5Vocabulary 11-1 Simplifying Algebraic Expressions term like term equivalent expressionsimplify
6Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsTerms in an expression are separated by plus or minus signs.Like terms can be grouped together because they have the same variable raised to the same power.Constants such as 4, 0.75, and 11 are like terms because none of them have a variable.Helpful HintEquivalent expressions have the same value for all values of the variables.
7Additional Example 1: Combining Like Terms To Simplify 11-1Simplifying Algebraic ExpressionsAdditional Example 1: Combining Like Terms To SimplifyCombine like terms.A. 14a – 5aIdentify like terms.9aCombine coefficients: 14 – 5 = 9Identify like terms ; the coefficient of y is 1, because 1y = y.B. 7y + 8 – 3y – 1 + yCombine coefficients: 7 – = 5 and 8 – 1 = 75y + 7
8Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsCheck It Out: Example 1Combine like terms.Identify like terms; the coefficient of q is 1, because 1q = q.A. 4q – q3qCombine coefficients: 4 – 1 = 3Identify like terms; the coefficient of c is 1, because 1c = c.B. 5c + 8 – 4c – 2 – cCombine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 66
9Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsAdditional Example 2A: Combining Like Terms in Two-Variables ExpressionsCombine like terms.9x + 3y – 2x + 59x + 3y – 2x + 5Identify like terms.7x + 3y + 5Combine coefficients: 9 – 2 = 7
10Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsAdditional Example 2B: Combining Like Terms in Two-Variable ExpressionsCombine like terms.5t + 7p – 3p – 2t5t + 7p – 3p – 2tIdentify like terms.Combine coefficients: 5 – 2 = 3 and 7 – 3= 43t + 4p
11Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsAdditional Example 2C: Combining Like Terms in Two-Variable ExpressionsCombine like terms.4m + 9n – 24m + 9n – 2No like terms.
12Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsCheck It Out: Example 2Combine like terms.A. 2x + 5x – 4y + 32x + 5x – 4y + 3Identify like terms.7x – 4y + 3Combine coefficients: = 7B. 9d + 7c – 4d – 2c9d + 7c – 4d – 2cIdentify like terms.5d + 5cCombine coefficients: 9 – 4 = 5 and 7 – 2 = 5C. 8g + c – 68g + c – 6No like terms.
13Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsTo simplify an expression, perform all possible operations, including combining like terms.The Distributive Property states that a(b + c) = ab + ac for all real numbers a, b, and c. For example, 2(3 + 5) = 2(3) + 2(5).Remember!
14Additional Example 3: Using the Distributive Property to Simplify 11-1Simplifying Algebraic ExpressionsAdditional Example 3: Using the Distributive Property to SimplifySimplify 6(5 + n) – 2n.6(5 + n) – 2n6(5) + 6(n) – 2nDistributive Property.30 + 6n – 2nMultiply.30 + 4nCombine coefficients 6 – 2 = 4.
16Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsAdditional Example 4: Combining Like Terms to Solve Algebraic EquationsSolve x + 3x = 48.x + 3x = 48Identify like terms. The coefficient of x is 1.4x = 48Combine coefficients: = 44x = 48Divide both sides by 4.44x = 12
17Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsCheck It Out: Example 4Solve 7c – c = 102.7c – c = 102Identify like terms. The coefficient of c is 1.6c = 102Combine coefficients: 7 – 1 = 66c = 102Divide both sides by 6.66c = 17
18Simplifying Algebraic Expressions 11-1Simplifying Algebraic ExpressionsLesson QuizCombine like terms.1. 3x x k + 6 8m kSimplify.3. 4(3x + 6) 7x (x + 5) + 3xSolve.5. 6y + y = 426. The accounting department ordered 15 boxes of pens. The marketing department ordered 9 boxes of pens. If the total cost of the combined order was $72, what is the price of each box of pens?5x + 414k – 8m + 155x + 249x + 30y = 6$3