Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Concept explainers

Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
Solve: = 25. We will use a property of equality to isolate the variable on one side of the equation. To solve the original equation, we want to find a simpler equivalent equation of the form x = a number, whose solution is obvious. To isolate x, we use the multiplication property of equality. We can undo the division by 3 by multiplying both sides by 3. 25 This is the equation to solve. 3 Multiply both sides by 3. = 3 3x = 75 Do the multiplications. Simplify 3x by removing the common factor of 3 in the numerator and denominator: = 1. 1x = X = The coefficient 1 need not be written since 1x = x. If we substitute 75 for x in 25, we obtain the true statement 25 = 25. This verifies that 75 is the solution. The solution set is {75}. Solve: b = 2. 28 b = m/3
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Transcribed Image Text:Solve: = 25. We will use a property of equality to isolate the variable on one side of the equation. To solve the original equation, we want to find a simpler equivalent equation of the form x = a number, whose solution is obvious. To isolate x, we use the multiplication property of equality. We can undo the division by 3 by multiplying both sides by 3. 25 This is the equation to solve. 3 Multiply both sides by 3. = 3 3x = 75 Do the multiplications. Simplify 3x by removing the common factor of 3 in the numerator and denominator: = 1. 1x = X = The coefficient 1 need not be written since 1x = x. If we substitute 75 for x in 25, we obtain the true statement 25 = 25. This verifies that 75 is the solution. The solution set is {75}. Solve: b = 2. 28 b = m/3
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