80 Chapter 1 Real Numbers and Algebraic Expressions �� ������������������������ ������������������ Simplify each algebraic expression. 4a. 3y - 5 + 8y - 1 4b. 3(4x + 2) - 8 4c. 2(4x - 5) + 3(2x - 1) 4d. 7 - 2(8x + 6) Solutions 4a. 3y - 5 + 8y - 1 = 3y + 8y - 5 - 1 Apply the commutative property. = 11y - 6 Combine like terms. 4b. 3(4x + 2) - 8 = 12 x + 6 - 8 Apply the distributive property. = 12x - 2 Combine like terms. 4c. 2(4x - 5) + 3(2x - 1) = 8x - 10 + 6x - 3 Apply the distributive property. = 8x + 6x - 10 - 3 Apply the commutative property. = 14x - 13 Combine like terms. 4d. 7 - 2(8x + 6) = 7 - 16x - 12 Apply the distributive property. =-16x + 7 - 12 Apply the commutative property. =-16x - 5 Combine like terms. Student Check 4 Simplify each algebraic expression. a. 4y - 8 - 2y b. 5(6x + 3) - 4 c. 6(3x + 1) + 4(5x - 3) d. 5 - 3(2x + 4) Troubleshooting Common Errors Some common errors associated with simplifying algebraic expressions are shown next. �� ������������������������ ������������������ A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 5a. Combine like terms: 5 + 2x �������������������������������������� ���������������������������������������������������������������� 5 + 2x 7x The terms 5 and 2x are not like terms. Therefore, they cannot be combined. The problem would have to be 5x + 2x to get an answer of 7x. 5b. Combine like terms: x2 + x2 �������������������������������������� ���������������������������������������������������������������� x2 + x2 x4 The terms are like. To add them, we must add their coefficients, not their exponents. Recall x2 = 1x2. x2 + x2 1x2 + 1x2 2x2 Objective 5 ▶ Troubleshoot common errors. 5 2 4
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