If the |x + 1| = 6, what are the possible values for x?

A.) -5 and 7

B.) -1 and 1

C.) 5 and -7

D.) 5 and -5

E.) 5 and 7

A.) -5 and 7

B.) -1 and 1

C.) 5 and -7

D.) 5 and -5

E.) 5 and 7

For a more basic example:

For a more basic example:

If |x| = 3,

then x could equal 3 or -3, because the absolute value of 3 is 3, and the absolute value of -3 is also 3

**|x + 1| = 6**

x + 1 = 6 or x + 1 = -6 {set the value of the expression inside the absolute value symbols equal to 6 and -6}

x = 5 or x = -7 {subtracted 1 from each side in both equations}

**C.) 5 and -7**are the possible values for x

Also if you take the original equation,

|x + 1| = 6, and subtract 6 from each side

|x + 1| - 6 = 0 {subtracted 6 from each side}

then graph the function, f(x) = |x + 1| - 6,

you can see that when the value of y {or f(x)}

is equal to 0 {also known as the x-intercept}

the value of x is, in fact, equal to -7 and 5, meaning

the graph crosses the x-axis at -7 and 5

*- Algebra House*