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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].
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