Absolute value
9 [9 - 8x] = 2× + 3
9 [9 -6×] =3
9 [-6x] = -6
54x = -6
x= -1/9 , × = 1/9
Is this correct? If not could you explain please.
Thank you
you need to get your typing straight
× is the symbol for multiplication
x is a variable name
9 (9 - 8x) = 2x + 3
81 - 72x = 2x + 3
78 = 74x
x = 78/74 = 39/37
Note that you cannot subtract the 2x inside the parentheses. You have to expand the left side first.
Try it with numbers:
3(2+5) = 19+2
Try subtracting the 2 as you did the 2x:
3(2+3) = 19 ???
And even if you could, -8x-2x = -10x
You titled it absolute value, so I will assume you are using "[" for absolute value.
I read your question as
9|9-8x| = 2x+3
then 9(9-8x) = 2x+3 OR 9(9-8x) = -2x-3
case1: 9(9-8x) = 2x+2 <--- Steve did that one
case2:
9(9-8x) = -2x-3
81 - 72x = -2x - 3
-70x = -84
x = 84/70 = 6/5
check:
LS = 9|9 - 8(6/5)|
= 9|-3/5| = 27/5
RS = 2(6/5)+3
= 27/5
= LS
so x = 39/37 (Steve's) or x = 6/5
http://www.wolframalpha.com/input/?i=solve+9%7C9-8x%7C+%3D+2x%2B3
To verify if your solution is correct, we can substitute the found values of x and × back into the original equation and check if both sides are equal.
Let's substitute the values:
For x = -1/9:
9[9 - 8(-1/9)] = 2(-1/9) + 3
9[9 + 8/9] = -2/9 + 3
9[81/9 + 8/9] = -2/9 + 27/9
9[89/9] = 25/9
89 = 25
For × = 1/9:
9[9 - 8(1/9)] = 2(1/9) + 3
9[9 - 8/9] = 2/9 + 3
9[81/9 - 8/9] = 2/9 + 27/9
9[73/9] = 29/9
73 = 29
As we can see, both values of x and × do not satisfy the equation. Therefore, your given solution is incorrect. Please recheck your calculations to find the correct solution.