absolute value

Question

So i have this worksheet and i dont understand it it has

13-2|x+3|=5 and it is saying to find the negative solution of the equation.

Howdo i find the Negitive solution to this equation?

Answer 1

When solving an absolute value problem, there will usually be two solutions, one positive and one negative. I will explain more when we get to that step of the problem...

13 - 2lx+3l = 5                             Given

13 - 2lx+3l -13 = 5 - 13                Subtract 13 from each side

-2lx + 3l = -8                               Simplify each side

-2lx + 3l/(-2) = -8/(-2)                  Divide each side by -2

lx + 3l = 4                                   Simplify

Whenever you have an absolute value isolated (it is on one side of the equation by itself), you can take the value inside the absolute value brackets and set it equal to the positive and negative values of what it is equal to.  If the absolute value is equal to a negative number, there is no solution.

x + 3 = 4   or        x + 3 = -4                    Equations created from the absolute value

x + 3 -3 = 4 - 3     x + 3 - 3 = -4 -3           Subtract 3 from each side

x = 1         or        x = -7                         Simplify

The negative solution is x = -7

Notice if you plug -7 into the original equation you will have

13 - 2l-7 + 3l = 5

13 - 2l-4l = 5

13 - 2(4) = 5

13 - 8 = 5

5 = 5

 

Answer 2

 The absolute value of an expression is always a non-negative result (positive or zero).  The expression inside the absolute value can be positive, zero, or negative.

Here is a little trick to use just this once. You won't need it once you understand. Let's create another variable, y, and let y=|x+3|. Now substitute into your problem.

13 - 2y = 5. Solve for y and you get y = 4. 

so since y = 4, and y=|x+3|, then |x+3|=4.  

Well we know that |4|=4 and |-4|=4 so either x+3 = 4 or x+3 = -4

x+3=4. Solve for x and x=1

x+3=-4. Solve for x and x=-7. This is your negative solution, the value of x which makes x+3=-4 true.

 

Answer 3

First, isolate the term with absolute value.

13-2|x+3|=5

Subtract 13 to both sides.

-2|x+3| = 5 - 13 = -8

Divide both sides by -2.

|x+3| = 18 / (-2) = 4

Second, split the absolute value equation into both cases (positive and negative).

|x+3| = 4

(x+3) = 4     and      -(x+3) = 4

x = 1             and    x = -7