Solve -0.58=x-30/frac{12{sqrt{25}}}

$$- 0.58 = \frac { x - 30 } { \frac { 12 } { \sqrt { 25 } } }$$

Solve for x

$$x=28.608$$

Steps for Solving Linear Equation

Divide x-30 by \frac{12}{\sqrt{25}} by multiplying x-30 by the reciprocal of \frac{12}{\sqrt{25}}.

$$-0.58=\frac{\left(x-30\right)\sqrt{25}}{12}$$

Calculate the square root of 25 and get 5.

$$-0.58=\frac{\left(x-30\right)\times 5}{12}$$

Use the distributive property to multiply x-30 by 5.

$$-0.58=\frac{5x-150}{12}$$

Divide each term of 5x-150 by 12 to get \frac{5}{12}x-\frac{25}{2}.

$$-0.58=\frac{5}{12}x-\frac{25}{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{5}{12}x-\frac{25}{2}=-0.58$$

Add \frac{25}{2} to both sides.

$$\frac{5}{12}x=-0.58+\frac{25}{2}$$

Convert decimal number -0.58 to fraction -\frac{58}{100}. Reduce the fraction -\frac{58}{100} to lowest terms by extracting and canceling out 2.

$$\frac{5}{12}x=-\frac{29}{50}+\frac{25}{2}$$

Least common multiple of 50 and 2 is 50. Convert -\frac{29}{50} and \frac{25}{2} to fractions with denominator 50.

$$\frac{5}{12}x=-\frac{29}{50}+\frac{625}{50}$$

Since -\frac{29}{50} and \frac{625}{50} have the same denominator, add them by adding their numerators.

$$\frac{5}{12}x=\frac{-29+625}{50}$$

Add -29 and 625 to get 596.

$$\frac{5}{12}x=\frac{596}{50}$$

Reduce the fraction \frac{596}{50} to lowest terms by extracting and canceling out 2.

$$\frac{5}{12}x=\frac{298}{25}$$

Multiply both sides by \frac{12}{5}, the reciprocal of \frac{5}{12}.

$$x=\frac{298}{25}\times \frac{12}{5}$$

Multiply \frac{298}{25} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{298\times 12}{25\times 5}$$

Do the multiplications in the fraction \frac{298\times 12}{25\times 5}.

$$x=\frac{3576}{125}$$