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Sagot :
To solve the equation [tex]\( 3 + \sqrt{2x + 4} = 7 \)[/tex], let's walk through the steps to isolate and solve for [tex]\( x \)[/tex]:
1. Isolate the square root term:
[tex]\[ 3 + \sqrt{2x + 4} = 7 \][/tex]
Subtract 3 from both sides to isolate the square root:
[tex]\[ \sqrt{2x + 4} = 7 - 3 \][/tex]
Simplify the right side:
[tex]\[ \sqrt{2x + 4} = 4 \][/tex]
2. Eliminate the square root by squaring both sides:
[tex]\[ (\sqrt{2x + 4})^2 = 4^2 \][/tex]
This leads to:
[tex]\[ 2x + 4 = 16 \][/tex]
3. Solve the resulting linear equation:
Subtract 4 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 2x = 16 - 4 \][/tex]
Simplify the right side:
[tex]\[ 2x = 12 \][/tex]
Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{12}{2} = 6 \][/tex]
Thus, the solution to the equation [tex]\( 3 + \sqrt{2x + 4} = 7 \)[/tex] is [tex]\(\boxed{6}\)[/tex]. The correct answer is option C: [tex]\( x = 6 \)[/tex].
1. Isolate the square root term:
[tex]\[ 3 + \sqrt{2x + 4} = 7 \][/tex]
Subtract 3 from both sides to isolate the square root:
[tex]\[ \sqrt{2x + 4} = 7 - 3 \][/tex]
Simplify the right side:
[tex]\[ \sqrt{2x + 4} = 4 \][/tex]
2. Eliminate the square root by squaring both sides:
[tex]\[ (\sqrt{2x + 4})^2 = 4^2 \][/tex]
This leads to:
[tex]\[ 2x + 4 = 16 \][/tex]
3. Solve the resulting linear equation:
Subtract 4 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 2x = 16 - 4 \][/tex]
Simplify the right side:
[tex]\[ 2x = 12 \][/tex]
Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{12}{2} = 6 \][/tex]
Thus, the solution to the equation [tex]\( 3 + \sqrt{2x + 4} = 7 \)[/tex] is [tex]\(\boxed{6}\)[/tex]. The correct answer is option C: [tex]\( x = 6 \)[/tex].
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