Solve the equation and write the solution set.
|4x – 8| – 3x = 6x + 2
I need help!!
|4x – 8| – 3x = 6x + 2
Either
(4x-8) - 3x = 6x+2
or
-(4x-8) - 3x = 6x+2
So, we have
x-8 = 6x+2
5x = -10
x = -2
or
-7x+8 = 6x+2
. . .
thx
To solve the given equation |4x – 8| – 3x = 6x + 2, we will first simplify the equation by removing the absolute value signs:
Considering the two cases:
1) 4x - 8 ≥ 0 ⇒ 4x ≥ 8 ⇒ x ≥ 2
Substituting back into the equation: (4x - 8) - 3x = 6x + 2
Simplifying: 4x - 8 - 3x = 6x + 2
x - 8 = 6x + 2
2) 4x - 8 < 0 ⇒ 4x < 8 ⇒ x < 2
Substituting back into the equation: -(4x - 8) - 3x = 6x + 2
Simplifying: -4x + 8 - 3x = 6x + 2
-7x + 8 = 6x + 2
Now, let's solve each case separately:
Case 1: x ≥ 2
Starting with the equation x - 8 = 6x + 2:
5x = -6
x = -6/5
However, since x ≥ 2 in this case, the solution x = -6/5 does not satisfy the inequality. Therefore, there are no solutions in this case.
Case 2: x < 2
Moving on to the equation -7x + 8 = 6x + 2:
-13x = -6
x = -6/-13
x = 6/13
Since x < 2 in this case, the solution x = 6/13 satisfies the inequality.
Therefore, the solution set for the given equation is x = 6/13.