Answer :
To solve the equation [tex]\(\sqrt{6x + 46} - 18 = -16\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Isolate the square root term:
[tex]\[ \sqrt{6x + 46} - 18 = -16 \][/tex]
Add 18 to both sides of the equation:
[tex]\[ \sqrt{6x + 46} = -16 + 18 \][/tex]
Simplify the right side:
[tex]\[ \sqrt{6x + 46} = 2 \][/tex]
2. Eliminate the square root by squaring both sides:
[tex]\[ (\sqrt{6x + 46})^2 = 2^2 \][/tex]
This simplifies to:
[tex]\[ 6x + 46 = 4 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Subtract 46 from both sides:
[tex]\[ 6x = 4 - 46 \][/tex]
Simplify the right side:
[tex]\[ 6x = -42 \][/tex]
Divide both sides by 6:
[tex]\[ x = \frac{-42}{6} \][/tex]
Simplify the fraction:
[tex]\[ x = -7 \][/tex]
Therefore, the solution to the equation is:
[tex]\[ \boxed{-7} \][/tex]
1. Isolate the square root term:
[tex]\[ \sqrt{6x + 46} - 18 = -16 \][/tex]
Add 18 to both sides of the equation:
[tex]\[ \sqrt{6x + 46} = -16 + 18 \][/tex]
Simplify the right side:
[tex]\[ \sqrt{6x + 46} = 2 \][/tex]
2. Eliminate the square root by squaring both sides:
[tex]\[ (\sqrt{6x + 46})^2 = 2^2 \][/tex]
This simplifies to:
[tex]\[ 6x + 46 = 4 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Subtract 46 from both sides:
[tex]\[ 6x = 4 - 46 \][/tex]
Simplify the right side:
[tex]\[ 6x = -42 \][/tex]
Divide both sides by 6:
[tex]\[ x = \frac{-42}{6} \][/tex]
Simplify the fraction:
[tex]\[ x = -7 \][/tex]
Therefore, the solution to the equation is:
[tex]\[ \boxed{-7} \][/tex]
