Absolute value equation |x-3|=5

x = - 2, x = 8

Step-by-step explanation:

The absolute value function always returns a positive value, but the expression inside can be positive or negative, thus

x - 3 = 5 OR - (x - 3) = 5

Solving both equations

x - 3 = 5 ( add 3 to both sides )

x = 8

OR

- x + 3 = 5 ( subtract 3 from both sides )

- x = 2 ( multiply both sides by - 1 )

x = - 2

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are solutions.

x = 8

| 8 - 3 | = | 5 | = 5 = right side

x = - 2

| - 2 - 3 | = | - 5 | = 5 = right side

Thus the solutions are x = - 2, x = 8

The equation given is the same as x - 3 = 5 or -(x - 3) = 5

Steps to solve:

x - 3 = 5

x - 3 + 3 = 5 + 3

x = 8

Steps to solve:

-(x - 3) = 5

-x + 3 = 5

-x + 3 - 3 = 5 - 3

-x = 2

-x/-1 = 2/-1

x = -2

Therefore, the solutions are x = 8 and x = -2

Best of Luck!

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.