Examples with solutions for Equations with Absolute Values: System of equations

Exercise #1

{x+2=x2x4=0 \begin{cases} |x+2|=|x-2| \\ x^4=0 \end{cases}

Video Solution

Answer

x=0 x=0

Exercise #2

{x111=5xgt;10 \begin{cases} ||x-11|-1|=5 \\ x>10 \end{cases}

Video Solution

Answer

x=17 x=17

Exercise #3

{x+3=2x+6x=3 \begin{cases} |x+3|=|2x+6| \\ \lvert x\rvert=3 \end{cases}

Video Solution

Answer

x=3 x=-3

Exercise #4

{x+2=x2x+2=0 \begin{cases} |x+2|=|x-2| \\ \lvert x+2\rvert=0 \end{cases}

Video Solution

Answer

No solution

Exercise #5

{x+4=2x+20xgt;10 \begin{cases} |x+4|=|2x+20| \\ x> -10 \end{cases}

Video Solution

Answer

x=8 x=-8

Exercise #6

{x+4=2x+20xlt;10 \begin{cases} |x+4|=|2x+20| \\ x < -10 \end{cases}

Video Solution

Answer

x=16 x=-16

Exercise #7

{x111=5x5=0 \begin{cases} ||x-11|-1|=5 \\ |x-5|=0 \end{cases}

Video Solution

Answer

x=5 x=5