Solve.
3 |4x−3|−3=8
I keep getting the wrong answer please help me
x=(5/3) & (-1/6)
Simply stating the answer is of no help to anybody.
3 |4x−3|−3=8
3 |4x−3|=11
|4x−3| = 11/3
(4x-3) = 11/3 OR -(4x-3) = 11/3
4x = 11/3 + 3 OR -4x = 11/3 - 3
4x = 20/3 OR -4x = 2/3
x = 5/3
or
x = - 1/6
To solve the equation 3|4x-3|-3 = 8, we need to isolate the absolute value term and then solve for x.
Let's break it down step by step:
1. Add 3 to both sides of the equation:
3|4x-3| - 3 + 3 = 8 + 3
3|4x-3| = 11
2. Divide both sides of the equation by 3:
(3|4x-3|) / 3 = 11 / 3
|4x-3| = 11/3
Now, there are two possible cases to consider when dealing with an absolute value: positive or negative.
Case 1: When the expression inside the absolute value is positive:
For |4x-3| = 11/3 to be positive, we can remove the absolute value notation and rewrite the equation as:
4x-3 = 11/3
Solve for x:
4x - 3 = 11/3
4x = 11/3 + 3
4x = 11/3 + 9/3
4x = 20/3
x = (20/3) / 4
x = 20/12
x = 5/3
Now, let's check if this solution holds true in the original equation.
Plugging x = 5/3 into the original equation:
3|4(5/3)-3|-3 = 8
Simplifying further:
3|(20/3)-3|-3 = 8
3|(20-9)/3|-3 = 8
3|(11/3)|-3 = 8
3|(11/3)| = 8 + 3
3|(11/3)| = 11
Since |11/3| equals 11/3, the left side becomes:
3 * (11/3) = 11
Therefore, the solution x = 5/3 satisfies the original equation.
Case 2: When the expression inside the absolute value is negative:
For |4x-3| = 11/3 to be negative, we can remove the absolute value notation and rewrite the equation as:
-(4x-3) = 11/3
Solve for x:
-4x + 3 = 11/3
-4x = 11/3 - 3
-4x = 11/3 - 9/3
-4x = 2/3
x = (2/3) / (-4)
x = (2/3) * (-1/4)
x = -2/12
x = -1/6
Now, let's check if this solution holds true in the original equation.
Plugging x = -1/6 into the original equation:
3|4(-1/6)-3|-3 = 8
Simplifying further:
3|-4/6-3|-3 = 8
3|-4/6-18/6|-3 = 8
3|-22/6|-3 = 8
3 * (22/6) - 3 = 8
11 - 3 = 8
8 = 8
Since both cases have been tested and the solutions hold true in the original equation, we have two solutions: x = 5/3 and x = -1/6.