Question

The following equation has how many solutions? \left|x-1\right|=7 ∣x−1∣=7

Answer 1

Answer:

Two solutions.

$x = 8, -6$

Step-by-step explanation:

Given the equation:

$\left|x-1\right|=7$

To find:

Number of solutions to the equation.

Solution:

First of all, let us learn about modulus function.

$|x|=\left \{ {{x\ if\ x>0} \atop {-x\ if\ x<0}} \right.$

i.e. Modulus function changes to positive by adding a negative sign to the negative values.

It has a value equal to $x$ when $x$ is positive.

It has a value equal to -$x$ when $x$ is negative.

Here, the function is:

$|x-1|=7$

So, two values are possible for the modulus function:

$\pm(x-1)=7$

Solving one by one:

$x-1 = 7\\\Rightarrow x =8$

$-(x-1) = 7\\\Rightarrow -x+1=7\\\Rightarrow x = -6$

So, there are two solutions, $x = 8, -6$