Question

How do you solve the absolute value equation $x + \left| x \right| = 28?$

Answer 1

Hint: Here we are given an expression in the form of absolute value and is given in the modulus so the values can be plus or minus of “x”. So, here we will frame two equations using the same concepts and will find the value for “x”.

Complete step-by-step solution:
Take the given expression: $x + \left| x \right| = 28$
Remove absolute value form and put instead plus or minus values for it.
$x \pm x = 28$
So, here we get two equations,
$x - x = 28$
Like terms with the same value and the opposite sign cancel each other.
$0 = 28$
The above equation is not possible.
$x + x = 28$
Simplify among the like terms.
$2x = 28$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$x = \dfrac{{28}}{2}$
Find factors on the numerator part of the equation on the right hand side of the equation.
$x = \dfrac{{2 \times 14}}{2}$
Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
$ \Rightarrow x = 14$
This is the required solution.

Note: Be good in multiples and find the factors of the numbers. Be careful about the sign convention while converting the absolute given equation and simplifying the equation. Remember basic rules while simplification of the like terms. Addition of two positive terms gives the positive term. Addition of one negative and positive term, you have to do subtraction and give signs of bigger numbers, whether positive or negative. Addition of two negative numbers gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.