1 6 Combining Like Terms Learn to combine

1 -6 Combining Like Terms Learn to combine like terms in an expression. Pre-Algebra

1 -6 Combining Like Terms 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. Equivalent expressions have the same value for all values of the variables. Pre-Algebra

1 -6 Combining Like Terms Example 1: Combining Like Terms To Simplify Combine like terms. A. 14 a – 5 a 9 a Identify like terms. B. 7 y + 8 – 3 y – 1 + y Identify like terms ; the coefficient of y is 1, because 1 y = y. 5 y + 7 Pre-Algebra Combine coefficients: 14 – 5 = 9 Combine coefficients: 7 – 3 + 1 = 5 and 8 – 1 = 7

1 -6 Combining Like Terms Example 2 A: Combining Like Terms in Two-Variables Expressions Combine like terms. A. 9 x + 3 y – 2 x + 5 Identify like terms. 7 x + 3 y + 5 Combine coefficients: 9 – 2 = 7 Pre-Algebra

1 -6 Combining Like Terms Example 2 B: Combining Like Terms in Two-Variable Expressions Combine like terms. B. 5 t + 7 p – 3 p – 2 t Identify like terms. 3 t + 4 p Combine coefficients: 5 – 2 = 3 and 7 – 3= 4 Pre-Algebra

1 -6 Combining Like Terms Example 2 C: Combining Like Terms in Two-Variable Expressions Combine like terms. C. 4 m + 9 n – 2 Pre-Algebra No like terms.

1 -6 Combining Like Terms 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. Equivalent expressions have the same value for all values of the variables. Pre-Algebra

1 -6 Combining Like Terms Try This: Example 1 Combine like terms. A. 4 q – q 3 q B. 5 c + 8 – 4 c – 2 – c 6 Pre-Algebra Identify like terms; the coefficient of q is 1, because 1 q = q. Combine coefficients: 4 – 1 = 3 Identify like terms; the coefficient of c is 1, because 1 c = c. Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6

1 -6 Combining Like Terms Try This: Example 2 Combine like terms. A. 2 x + 5 x – 4 y + 3 Identify like terms. 7 x – 4 y + 3 Combine coefficients: 2 + 5 = 7 B. 9 d + 7 c – 4 d – 2 c Identify like terms. 5 d + 5 c Combine coefficients: 9 – 4 = 5 and 7 – 2 = 5 C. 8 g + c – 6 Pre-Algebra No like terms.

1 -6 Combining Like Terms To simplify an expression, perform all possible operations, including combining like terms. Pre-Algebra

1 -6 Combining Like Terms Example 3: Simplifying Algebraic Expressions by Combining Like Terms Simplify 6(5 + n) – 2 n 6(5) + 6(n) – 2 n Distributive Property. 30 + 6 n – 2 n 6 n and 2 n are like terms. 30 + 4 n Combine coefficients 6 – 2 = 4 Pre-Algebra

1 -6 Combining Like Terms Example 4: Solving Algebraic Expressions by Combining Like Terms Solve x + 3 x = 48 4 x = 48 Combine coefficients: 1 + 3 = 4 4 x = 48 4 4 Divide both sides by 4. x = 12 Pre-Algebra Identify like terms. The coefficient of x is 1.

1 -6 Combining Like Terms 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. Equivalent expressions have the same value for all values of the variables. Pre-Algebra

1 -6 Combining Like Terms To simplify an expression, perform all possible operations, including combining like terms. Pre-Algebra

1 -6 Combining Like Terms Try This: Example 1 Combine like terms. A. 4 q – q 3 q B. 5 c + 8 – 4 c – 2 – c 6 Pre-Algebra Identify like terms; the coefficient of q is 1, because 1 q = q. Combine coefficients: 4 – 1 = 3 Identify like terms; the coefficient of c is 1, because 1 c = c. Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6

1 -6 Combining Like Terms Try This: Example 2 Combine like terms. A. 2 x + 5 x – 4 y + 3 Identify like terms. 7 x – 4 y + 3 Combine coefficients: 2 + 5 = 7 B. 9 d + 7 c – 4 d – 2 c Identify like terms. 5 d + 5 c Combine coefficients: 9 – 4 = 5 and 7 – 2 = 5 C. 8 g + c – 6 Pre-Algebra No like terms.

1 -6 Combining Like Terms Try This: Example 3 Simplify 3(c + 7) – c 3(c) + 3(7) – c Distributive Property. 3 c + 21 – c 3 c and c are like terms. 2 c + 21 Combine coefficients 3 – 1 = 2 Pre-Algebra

1 -6 Combining Like Terms Try This: Example 4 Solve 7 c – c = 102 Identify like terms. The coefficient of c is 1. 6 c = 102 Combine coefficients: 7 – 1 = 6 6 c = 102 6 6 Divide both sides by 6. c = 17 Pre-Algebra