Solve -5126=-6-5(3x+22)5/3

$$-5126=-6-5(3x+22) \frac{ 5 }{ 3 }$$

Solve for x

$$x = \frac{2962}{15} = 197\frac{7}{15} \approx 197.466666667$$

Steps for Solving Linear Equation

Express 5\times \frac{5}{3} as a single fraction.

$$-5126=-6-\frac{5\times 5}{3}\left(3x+22\right)$$

Multiply 5 and 5 to get 25.

$$-5126=-6-\frac{25}{3}\left(3x+22\right)$$

Use the distributive property to multiply -\frac{25}{3} by 3x+22.

$$-5126=-6-\frac{25}{3}\times 3x-\frac{25}{3}\times 22$$

Cancel out 3 and 3.

$$-5126=-6-25x-\frac{25}{3}\times 22$$

Express -\frac{25}{3}\times 22 as a single fraction.

$$-5126=-6-25x+\frac{-25\times 22}{3}$$

Multiply -25 and 22 to get -550.

$$-5126=-6-25x+\frac{-550}{3}$$

Fraction \frac{-550}{3} can be rewritten as -\frac{550}{3} by extracting the negative sign.

$$-5126=-6-25x-\frac{550}{3}$$

Convert -6 to fraction -\frac{18}{3}.

$$-5126=-\frac{18}{3}-25x-\frac{550}{3}$$

Since -\frac{18}{3} and \frac{550}{3} have the same denominator, subtract them by subtracting their numerators.

$$-5126=\frac{-18-550}{3}-25x$$

Subtract 550 from -18 to get -568.

$$-5126=-\frac{568}{3}-25x$$

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

$$-\frac{568}{3}-25x=-5126$$

Add \frac{568}{3} to both sides.

$$-25x=-5126+\frac{568}{3}$$

Convert -5126 to fraction -\frac{15378}{3}.

$$-25x=-\frac{15378}{3}+\frac{568}{3}$$

Since -\frac{15378}{3} and \frac{568}{3} have the same denominator, add them by adding their numerators.

$$-25x=\frac{-15378+568}{3}$$

Add -15378 and 568 to get -14810.

$$-25x=-\frac{14810}{3}$$

Divide both sides by -25.

$$x=\frac{-\frac{14810}{3}}{-25}$$

Express \frac{-\frac{14810}{3}}{-25} as a single fraction.

$$x=\frac{-14810}{3\left(-25\right)}$$

Multiply 3 and -25 to get -75.

$$x=\frac{-14810}{-75}$$

Reduce the fraction \frac{-14810}{-75} to lowest terms by extracting and canceling out -5.

$$x=\frac{2962}{15}$$