Linear Equations and Inequalities - XYZ Custom Plus

2.1 Simplifying Expressions115As you can see from the explanation in Example 9, we use the distributiveproperty to simplify expressions in which parentheses are preceded by a negativesign. In general we can write−(a + b) = −1(a + b)= −a + (−b)= −a − bThe negative sign outside the parentheses ends up changing the sign of eachterm within the parentheses. In words, we say “the opposite of a sum is the sumof the opposites.”C The Value of an ExpressionRecall from Chapter 1, an expression like 3x + 2 has a certain value depending onwhat number we assign to x. For instance, when x is 4, 3x + 2 becomes 3(4) + 2,or 14. When x is −8, 3x + 2 becomes 3(−8) + 2, or −22. The value of an expressionis found by replacing the variable with a given number.ExamplesFind the value of the following expressions by replacingthe variable with the given number.Value ofValue ofExpression the Variable the Expression10. 3x − 1 x = 2 3(2) − 1 = 6 − 1 = 511. 7a + 4 a = −3 7(−3) + 4 = −21 + 4 = −1712. 2x − 3 + 4x x = −1 2(−1) − 3 + 4(−1)= −2 − 3 + (−4) = −913. 2x − 5 − 8x x = 5 2(5) − 5 − 8(5)= 10 − 5 − 40 = −3514. y 2 − 6y + 9 y = 4 4 2 − 6(4) + 9 = 16 − 24 + 9 = 110. Find the value of 4x − 7 whenx = 3.11. Find the value of 2a + 4 whena = −5.12. Find the value of 2x − 5 + 6xwhen x = −2.13. Find the value of 7x − 3 − 4xwhen x = 10.14. Find the value of y 2 − 10y + 25when y = −2.Simplifying an expression should not change its value; that is, if an expressionhas a certain value when x is 5, then it will always have that value no matter howmuch it has been simplified, as long as x is 5. If we were to simplify the expressionin Example 13 first, it would look like2x − 5 − 8x = −6x − 5When x is 5, the simplified expression −6x − 5 is−6(5) − 5 = −30 − 5 = −35It has the same value as the original expression when x is 5.We also can find the value of an expression that contains two variables if weknow the values for both variables.Answers10. 5 11. −6 12. −21 13. 2714. 49