Write an absolute value equation that has the solutions x=8 and x=18.

|x - 13| = 5

Step-by-step explanation:

Think of absolute value as a distance. For example, |5| can be written as |5 - 0| = 5 since the distance between 5 and zero on the number line is 5. Also, |-5| which is the same as |-5 - 0| is also 5 since the distance between -5 and zero on the number line is 5.

Since you want an absolute value equation with solutions 8 and 18, think of which number is the same distance from both 8 and 18 on the number line? Find the average of 8 and 18, (8 + 18)/2 = 13. 13 is the same distance from both 8 and 18. 13 is 5 units away from both 8 and 18. Now you need an equation that is looking for the numbers x which are 5 units distance from 13.

|x - 13| = 5

Here we want to find an absolute value equation only by knowing its solutions. We will find that the function is |x - 13| = 5

We want an absolute value equation with solutions x = 8 and x = 18.

Remember that a general absolute value equation can be written as:

|x - a| = b

We can rewrite this in two equations:

x - a = b

x - a = -b

Now let's replace the known solutions in the image, we should use the larger value of x in the equation with the positive b.

18 - a = b

8 - a = -b

This is a system of equations, to solve this, we can rewrite the second equation as:

8 -a = -b

-8 + a = b

Now we can replace this in the first equation:

18 - a = b = -8 + a

18 - a = -8 + a

18 + 8  = a + a

26 = 2a

26/2 = a = 13

Now we know the value of a, then we can use the equation:

18 - 13 = b = 5

Then the absolute value equation is:

|x - 13| = 5

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found it xd it ok yt

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: