First, we will solve for the positive value inside the absolute value.
9 - 8x = 2x + 3.
We will start solving for x by combining like terms:
9 - 3 = 2x + 8x.
6 = 10x.
Next, we divide both sides by 10 to solve for x:
6/10 = 10x/10,
0.6 = x.
So, x = 0.6 is a potential solution.
Now, we will solve for the negative value inside the absolute value:
-(9 - 8x) = 2x + 3.
We will start solving for x by distributing the negative sign:
-9 + 8x = 2x + 3.
Next, we will combine like terms:
8x - 2x = 3 + 9,
6x = 12.
Dividing both sides by 6:
x = 12/6,
x = 2.
So, x = 2 is another potential solution.
Now, we will check for extraneous solutions by substituting each potential solution back into the original equation:
For x = 0.6:
9|9 - 8(0.6)| = 2(0.6) + 3,
9|9 - 4.8| = 1.2 + 3,
9|4.2| = 4.2 + 3,
9(4.2) = 7.2,
37.8 = 7.2,
This is not true, so x = 0.6 is an extraneous solution and is not a solution to the equation.
For x = 2:
9|9 - 8(2)| = 2(2) + 3,
9|9 - 16| = 4 + 3,
9|-7| = 7,
9(7) = 7,
63 = 7,
This is not true, so x = 2 is an extraneous solution and is not a solution to the equation.
Therefore, the equation has no real solutions.
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Solve the equation. Check for extraneous solutions.
9|9−8x|=2x+3
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