Given the equation square root of quantity 3x plus 4 end quantity equals 5, solve for x and identify if it is an extraneous solution. 7; solution is not extraneous 7; solution is extraneous four thirds; solution is not extraneous four thirds; solution is extraneous

Accepted Solution

Answer:7; solution is not extraneousStep-by-step explanation:we have[tex]\sqrt{3x+4}=5[/tex]Solve for xsquared both sides[tex](\sqrt{3x+4})^2=5^2[/tex][tex]3x+4=25[/tex]subtract 4 both sides[tex]3x=25-4[/tex][tex]3x=21[/tex]Divide by 3 both sides[tex]x=7[/tex]VerifySubstitute the value of x in the original equation[tex]\sqrt{3(7)+4}=5[/tex][tex]\sqrt{21+4}=5[/tex][tex]\sqrt{25}=5[/tex][tex]5=5[/tex] ----> is truethereforeThe value of x=7 is a solution, Is not a extraneous