Solve |4x−5|=|−x+5| by graphing
does this help? The result can be shown in multiple forms.
Exact Form:
x
=
−
4
,
−
1
3
Decimal Form:
x
=
−
4
,
−
0.
¯
3
check out mathway
Cannot graph on these posts.
oh, well like i said, check out mathway. a lot more help then my chicken like brain lol
To solve the equation |4x−5|=|−x+5| by graphing, you need to plot the graphs of both sides of the equation and find the points of intersection.
First, let's start by graphing the left side of the equation, |4x−5|. This equation represents the absolute value of (4x−5).
1. Find the x-intercept of the equation: Setting 4x−5 to zero and solving for x, we get:
4x−5 = 0
4x = 5
x = 5/4
So, the x-intercept is at (5/4, 0).
2. Find the y-intercept of the equation: Plug in x = 0 into the equation:
|4(0)−5|
|-5|
5
So, the y-intercept is at (0, 5).
Plot these two points on the graph.
Next, let's graph the right side of the equation, |−x+5|. This equation represents the absolute value of (−x+5).
1. Find the x-intercept of the equation: Setting −x+5 to zero and solving for x, we get:
−x+5 = 0
−x = −5
x = 5
So, the x-intercept is at (5, 0).
2. Find the y-intercept of the equation: Plug in x = 0 into the equation:
|−(0)+5|
|5|
5
So, the y-intercept is at (0, 5).
Plot these two points on the graph.
Now, we have two lines on the graph representing the two sides of the equation. To solve the equation, look for the points of intersection between the two lines. The coordinates of these points represent the solutions to the equation.
In this case, you will notice that the two lines are the same line. Therefore, they intersect at all points of the line. This means that the solution to the equation |4x−5|=|−x+5| is x = any real number.
To summarize, the solution to the equation |4x−5|=|−x+5| by graphing is x = any real number.