We have the following equation:
[tex]\sqrt{x-5} +7=11[/tex]
To solve this, we first need to subtract the 7 on both sides of the equation.
[tex]\sqrt{x-5} +7-7=11-7[/tex]
The equation then becomes:
[tex]\sqrt{x-5} =4[/tex]
Now we must square both sides of the equation to get rid of the radical/square root symbol.
[tex](\sqrt{x-5})^2 =(4)^2[/tex]
Now we have a normal one step equation.
[tex]x-5=16[/tex]
Add 5 on both sides to find x.
[tex]x-5+5=16+5[/tex]
x=21
To see if this solution is true, we must substitute 21 back into the original equation.
[tex]\sqrt{21-5} +7=11[/tex]
[tex]\sqrt{16} +7=11[/tex]
[tex]4+7=11[/tex]
11=11
Therefore, the solution is true.
