Solve 3^2x+1=1/9

$${ 3 }^{ 2 } x+1= \frac{ 1 }{ 9 }$$

Solve for x

$$x=-\frac{8}{81}\approx -0.098765432$$

Steps for Solving Linear Equation

Calculate 3 to the power of 2 and get 9.

$$9x+1=\frac{1}{9}$$

Subtract 1 from both sides.

$$9x=\frac{1}{9}-1$$

Convert 1 to fraction \frac{9}{9}.

$$9x=\frac{1}{9}-\frac{9}{9}$$

Since \frac{1}{9} and \frac{9}{9} have the same denominator, subtract them by subtracting their numerators.

$$9x=\frac{1-9}{9}$$

Subtract 9 from 1 to get -8.

$$9x=-\frac{8}{9}$$

Divide both sides by 9.

$$x=\frac{-\frac{8}{9}}{9}$$

Express \frac{-\frac{8}{9}}{9} as a single fraction.

$$x=\frac{-8}{9\times 9}$$

Multiply 9 and 9 to get 81.

$$x=\frac{-8}{81}$$

Fraction \frac{-8}{81} can be rewritten as -\frac{8}{81} by extracting the negative sign.

$$x=-\frac{8}{81}$$