Find trusted answers to your questions with the help of IDNLearn.com's knowledgeable community. Discover reliable and timely information on any topic from our network of experienced professionals.

Solve the equation for [tex]$x$[/tex].

[tex]\sqrt{x+4} - 7 = 1[/tex]

A. [tex]x = 4[/tex]
B. [tex]x = 12[/tex]
C. [tex]x = 60[/tex]
D. [tex]x = 68[/tex]


Sagot :

Let's solve the equation:
[tex]\[ \sqrt{x + 4} - 7 = 1 \][/tex]

Step 1: Isolate the square root term.
[tex]\[ \sqrt{x + 4} - 7 = 1 \implies \sqrt{x + 4} = 1 + 7 \][/tex]

Step 2: Simplify the right side of the equation.
[tex]\[ \sqrt{x + 4} = 8 \][/tex]

Step 3: Square both sides of the equation to eliminate the square root.
[tex]\[ (\sqrt{x + 4})^2 = 8^2 \implies x + 4 = 64 \][/tex]

Step 4: Solve for [tex]\(x\)[/tex] by isolating it on one side of the equation.
[tex]\[ x + 4 = 64 \implies x = 64 - 4 \implies x = 60 \][/tex]

Therefore, the solution to the equation [tex]\(\sqrt{x + 4} - 7 = 1\)[/tex] is:
[tex]\[ x = 60 \][/tex]

Among the given options, the correct answer is [tex]\(x = 60\)[/tex].