I've to solve the following absolute value equation 8|w-7|=72.
I solved the equation and the answers I got were -2 and 16. However the problem is that when I'm checking the equation with the answers it's not coming right.
I.E.
8|16-7|=72
8|9| = 72
8(9)= 72
72 = 72 (which is right)
8|-2-7|=-72
8|-9| = -72
8 (9) = - 72
72 = -72 (its coming wrong)
Thus is the second equation right and am I solving it in the right way?
Sorry! I got it now! I was solving it the wrong way! silly me! :p:) Sorry to bother you!
Nice work! Both of your solutions are correct. Thanks for rechecking (and doing) your own work! It makes our job easier.
To solve the absolute value equation 8|w-7|=72, you need to follow the correct steps. Let's go through the solution process together:
Step 1: Remove the absolute value by setting up two separate equations:
1) w - 7 = 72/8
2) -(w - 7) = 72/8
Step 2: Solve each equation separately.
For equation 1:
w - 7 = 9
Add 7 to both sides:
w = 16
For equation 2:
-(w - 7) = 9
Distribute the negative sign:
-w + 7 = 9
Subtract 7 from both sides:
-w = 2
Now, multiply both sides by -1 to isolate w:
w = -2
So far, you have found w = 16 and w = -2 as potential solutions.
Now, let's check these solutions to verify if they are correct:
Check for w = 16:
8|16 - 7| = 72
8|9| = 72
8 * 9 = 72
72 = 72 (The equation is true for this value.)
Check for w = -2:
8|-2 -7| = 72
8|-9| = 72
8 * 9 = 72
72 = 72 (The equation is also true for this value.)
Upon rechecking, you can see that both solutions, w = 16 and w = -2, satisfy the original equation. Both of your previous answers are correct.
Sometimes errors can occur while checking equations, so please double-check your calculations and make sure you are evaluating expressions accurately.