Why is the answer in math way 7,-1?

Question

(x-3)=4

The parenthesis is actually an absolute value sign.

x-3=4

x=7

but how does it give you -1?

Answer 1

If the parentheses are absolute value signs, that means the value of x-3 that results in negative 4 or positive 4 will be correct.  Absolute value means the value of the number, whether it is positive or negative. 

 

If you look at a number line as a ruler....and you are standing on the zero...if you move to the positive four position, you have moved "4" spaces.  If you move to the negative four position, you have moved "4" spaces.  This is how I look at absolute value. 

 

so, to solve your equation, it becomes two: (x-3)=4, or -(x-3)=4.

 

the first one is easy; x-3+3=4+3

                              x=7

the second is a bit trickier:  think of it as negative one multiplied by (x-3).  Use the distributive property to make the equation:

-1(x-3) =4

-1 (x + -3) =4

-1x + (-1)(-3) =4

-1x +3 =4

-1x +3 -3 =4-3

-1x=1

-1x/-1= 1/-1

 

x=-1

Answer 2

|x-3| = 4

 

If x-3 = 4 then the equation is true.  If x-3 = -4, then it's also true because |-4|=4.  So there are two ways to satisfy the absolute value equation, x-3 = 4 and x-3 = -4.  Solve each one separately:

 

    x-3 = 4

    x = 7

 

    x-3 = -4

    x = -1

 

Both values, x=7 and x = -1, satisfy the absolute value equation.  To verify, plug each of them back into the original equation.

Answer 3

|x - 3| = 4

 

The number inside the absolute value sign can be either positive or negative. Therefore, the equation must be solved twice: one as if the number is positive and once as if the number is negative.

 

I. x - 3 ≥ 0

x - 3 = 4

x = 7

 

II. x - 3 < 0

-(x - 3) = 4        multiply both sides by -1

x - 3 = -4          add 3 to both sides

x = -1

 

x ∈ {-1, 7}