Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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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.
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**Geometry Problem: Solving for x** **Problem Statement:** The two lines below intersect as shown. What is the value of x? **Diagram Explanation:** The diagram shows two intersecting lines forming an X shape. At the top left of the intersection, the angle is labeled \((2x + 29)^\circ\). At the top right of the intersection, the angle is labeled \((9x - 13)^\circ\). \[(2x + 29)^\circ \quad (9x - 13)^\circ\] The possible answer choices are: - 6 - 9 - 12 - 4 **Details for Calculation:** Given that the angles opposite each other are congruent, the equation to solve for \(x\) is: \[2x + 29 = 9x - 13\] Solving for \(x\): 1. Subtract \(2x\) from both sides: \[29 = 7x - 13\] 2. Add 13 to both sides: \[42 = 7x\] 3. Divide both sides by 7: \[x = 6\] Therefore, the correct value of \(x\) is 6.
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Transcribed Image Text:**Geometry Problem: Solving for x** **Problem Statement:** The two lines below intersect as shown. What is the value of x? **Diagram Explanation:** The diagram shows two intersecting lines forming an X shape. At the top left of the intersection, the angle is labeled \((2x + 29)^\circ\). At the top right of the intersection, the angle is labeled \((9x - 13)^\circ\). \[(2x + 29)^\circ \quad (9x - 13)^\circ\] The possible answer choices are: - 6 - 9 - 12 - 4 **Details for Calculation:** Given that the angles opposite each other are congruent, the equation to solve for \(x\) is: \[2x + 29 = 9x - 13\] Solving for \(x\): 1. Subtract \(2x\) from both sides: \[29 = 7x - 13\] 2. Add 13 to both sides: \[42 = 7x\] 3. Divide both sides by 7: \[x = 6\] Therefore, the correct value of \(x\) is 6.
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