Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Review - Concept Check - Page 133: 38

Answer

i) When solving an equation algebraically, in most cases, the goal is to isolate the single variable in the equation. For example, to get x by itself in the equation 6x-4=20 you would have to first add 4 on each side to get 6x=24 and then divide by 6 to isolate x and get an answer of x=4. Isolating the variable uses many operations like adding, subtracting, dividing, and multiplying. Algebraically it is possible to plug in the answer you solved to verify if you were right. In our example, that would mean 6(4)-4=20, which ends up being 20=20. When both sides of the equation are the same, that means the answer you got was correct. ii) Solving an equation graphically is usually done when 1) the equation is not given and you must find a specific value or 2) you are not able to solve an equation with the tools you have learned yet. For example, if a problem asked how much money you had after two hours and only a graph was given, then you would look at the value of 2 on the x-axis and see what y-value it was on the graph. Now let's say you were asked to solve the equation log(x)+3x= x-9. If you did not know what log(x) was, then this system of equations would not be able to be solved algebraically. Here we have two equations, y= log(x) +3x and y=x-9, that can be graphed separately. After graphing the two equations, we can look at where the two intersection. The point of intersection is the answer.

Work Step by Step

Refer to the first explanation
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.