the solutions to the equation [tex]5 = |8 - x|[/tex] is [tex]x= 3[/tex] & [tex]x= 13[/tex] .
Step-by-step explanation:
Here we have , Georgia has a budget of $8 for a new notebook. She wants to spend within $5 of her budget, so she uses the equation 5 = |8 – x| to find the maximum and minimum values. We need to find What are the solutions to the equation . Let's find out:
We have following , equation to solve : 5 = |8 – x|
Case 1 . Modulus is positive
We have ,
⇒ [tex]5 = |8 - x|[/tex]
⇒ [tex]5 = 8 - x[/tex]
⇒ [tex]x= 8 - 5[/tex]
⇒ [tex]x= 3[/tex]
Case 2. Modulus is negative
We have ,
⇒ [tex]5 = |8 - x|[/tex]
⇒ [tex]5 = -(8 - x)[/tex]
⇒ [tex]x= 8 + 5[/tex]
⇒ [tex]x= 13[/tex]
Therefore , the solutions to the equation [tex]5 = |8 - x|[/tex] is [tex]x= 3[/tex] & [tex]x= 13[/tex] .
