Question

Solve the equation

∣x−2∣=∣4+x |

x=

Answer 1

`\large\boxed{\mathtt{x=-1}}`

Explanation:

`\textsf{For this problem, we are asked to solve the equation for x.}`

`\textsf{Note that there are lines in between both expressions, this is asking for the \underline{Absolute Value}.}`

`\large\underline{\textsf{What is Absolute Value?}}`

`\textsf{Absolute Value is exactly how it sounds like, it's the real value of a term.}`

`\textsf{Absolute Value turns negative numbers into positive numbers.}`

`\textsf{*A Negative Value isn't really the real value of a number. A Positive Value is.}`

`\underline{\textsf{Example;}}`

`\tt {Change \ from \ Negative \ to \ Positive.} \atop \boxed{}`

`\large\underline{\textsf{Keep the Absolute Values!}}`

`\textsf{We shouldn't try to find the absolute value of the expressions first.}`

`\textsf{Instead, identify 2 possible equations using Absolute Value.}`

`\textsf{There could be 2 possible solutions for x.}`

`\tt x-2=4+x`

`\underline{\textsf{Or;}}`

`\tt x-2=-(4+x)`

`\large\underline{\textsf{Solve the First equation;}}`

`\tt x-2=4+x`

`\underline{\textsf{Add 2 to both sides of the equation;}}`

`\tt x=6+x`

`\textsf{There is \underline{no} solution for this equation. We should look at the second equation.}`

`\large\underline{\textsf{Solve the Second equation;}}`

`\tt x-2=-4-x`

`\underline{\textsf{Add 4 to both sides of the equation;}}`

`\tt x=-x-2`

`\underline{\textsf{Add x to both sides of the equation;}}`

`\tt 2x=-2`

`\underline{\textsf{Divide each side by 2;}}`

`\large\boxed{\mathtt{x=-1}}`

`\textsf{Using Absolute Value, x = -1.}`