32 Chapter 1 Real Numbers and Algebraic Expressions �� ������������������������ ������������������ Determine if the given value is a solution of the equation. 4a. 4y + 5 = y2; y = 5 4b. 3x - 2(x + 1) = x + 5; x = 4 Solutions 4a. 4y + 5 = y2 4(5) + 5 = (5)2 Replace y with 5. 20 + 5 = 25 Multiply 4 and 5 and simplify 52. 25 = 25 Add. Since y = 5 makes the equation true, it is a solution of 4y + 5 = y2. 4b. 3x - 2(x + 1) = x + 5 3(4) - 2(4 + 1) = 4 + 5 Replace x with 4. 12 - 2(5) = 9 Multiply 3 and 4. Add in parentheses and on the right side.. 12 - 10 = 9 Multiply 2 and 5. 2 = 9 Simplify. Since x = 4 makes the equation false, it is not a solution of 3x - 2(x + 1) = x + 5. Student Check 4 Determine if the given value is a solution of the equation. a. a2 - a + 6 = a - 2; a = 4 b. 7b - 5(b + 2) = b + 3; b = 13 Translate Expressions into Symbols Now that we know how to evaluate an algebraic expression, we will turn our focus on how to express or write mathematical relationships given certain phrases or sentences. The following table shows some common phrases for the basic mathematical expressions. Addition a + b sum of a and b a increased by b b more than a a added to b a plus b Subtraction a - b difference of a and b b subtracted from a b less than a a minus b a decreased by b from a, subtract b Multiplication ab product of a and b a times b a multiplied by b a of b Division a b a divided by b quotient of a and b ratio of a to b Equation a = b a is b a is equal to b a yields b The result of a is the same as b Objective 5 ▶ Express relationships mathematically.
hendricks_beginning_algebra_1e_ch1_3
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