so with this one i do the same thing multiplying what inside absolute value bracket bar with what outside?
|2x-8|-2 = 4x
so that start me off as -4x+16 = 4x or 4x-16 = 4x.
solve equation |x^2-2x-6| = 4
this nothing to do with factoring right? i just add six to both sides and add 2x to both sides?
it actually say to use quadratic formula so i subtract 4 from both sides to get an equation by itself so i plug it in?
there are no x^2 terms, so no quadratic formula. This was answered already - see the links below.
To solve the equation |2x-8|-2 = 4x, you need to consider the two possible cases when the expression inside the absolute value brackets is positive and when it is negative.
1. Case 1: When 2x-8 is positive:
In this case, you should keep the value inside the absolute value brackets as it is.
|2x-8| = 2x-8
-2 + 2x-8 = 4x (Replace |2x-8| with 2x-8)
Simplifying the equation:
2x - 10 = 4x
-10 = 2x
x = -5
2. Case 2: When 2x-8 is negative:
In this case, you should multiply the value inside the absolute value brackets by -1 to make it positive.
|2x-8| = -(2x-8) = -2x+8
-2x + 8 -2 = 4x (Replace |2x-8| with -2x+8)
Simplifying the equation:
-2x + 6 = 4x
6 = 6x
x = 1
So the solutions to the equation are x = -5 and x = 1.
Moving on to the equation |x^2-2x-6| = 4, you can solve it by considering two cases as well.
1. Case 1: When x^2-2x-6 is positive:
In this case, you should leave the value inside the absolute value brackets as it is.
x^2-2x-6 = 4
Rearranging the equation:
x^2 - 2x - 10 = 0
To solve this quadratic equation, you can factor it or use the quadratic formula.
2. Case 2: When x^2-2x-6 is negative:
In this case, you need to multiply the value inside the absolute value brackets by -1 to make it positive.
|x^2-2x-6| = -(x^2-2x-6) = -x^2+2x+6
-x^2 + 2x + 6 = 4
Rearranging the equation:
-x^2 + 2x + 2 = 0
Again, you can solve this quadratic equation by factoring or using the quadratic formula.
So solving the equation |x^2-2x-6| = 4 involves the use of factoring or the quadratic formula, there's no need for adding 6 to both sides or adding 2x to both sides.