Question

How do you solve $ - \left| {x + 1} \right| = - 2$

Answer 1

Hint: The $\left| {} \right|$is the symbol called modulus. Which changes the negative values to positive.
The modulus is an operation done on numbers. If the value is less than zero, the modulus would be negative, if the value is more than zero, the modulus would be positive value. The graph of modulus will give a sharp centre.

Complete step-by-step answer:
Given,
The value is in modulus. We need to calculate the value of x.
$ - \left| {x + 1} \right| = - 2$
As we already know that the modulus can give both negative and positive values because the x is inside the modulus. So there will be two values for x.
We need to find two values for x.
First, if the modulus is positive value,
$\left| {x + 1} \right| = x + 1$
Substitute modulus value in equation,
$ - \left( {x + 1} \right) = - 2$
Multiply $ - 1$ in above equation,
$
   - (x + 1) \times - 1 = - 2 \times - 1 \\
  x + 1 = 2 \\
 $
To find the value of x bring values from left side to right side of the equation,
$x = 2 - 1$
Subtract the above equation
$x = 1$
Here we found the answer for modulus is positive. Hence we need to find a negative value of modulus.
If the modulus is negative value,
$\left| {x + 1} \right| = - (x + 1)$
Substitute modulus value in equation
$ - ( - \left( {x + 1} \right)) = - 2$
Multiply $ - 1$ in above equation
$x + 1 = - 2$
To find the value of x bring values from left side to right side of the equation,
$x = - 2 - 1$
Subtract the values in above equation
$x = - 3$
Here we found the value of x when the modulus has a negative value.
As the modulus gives both negative and positive value, it has two unique solutions $x = 1$ or $x = - 3$

Note: The modulus must be taken into consideration as it gives two values (both positive and negative values). The values should be correctly operated. Correct sign should be used. Both values must be written in answer. All the terms in the question must be correctly checked once or twice because change in one term will lead to the wrong answer.