Solve -4(14/3-2)-7y=15

$$- 4 ( \frac { 14 } { 3 } - 2 ) - 7 y = 15$$

Solve for y

$$y = -\frac{11}{3} = -3\frac{2}{3} \approx -3.666666667$$

Steps for Solving Linear Equation

Convert 2 to fraction \frac{6}{3}.

$$-4\left(\frac{14}{3}-\frac{6}{3}\right)-7y=15$$

Since \frac{14}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$-4\times \frac{14-6}{3}-7y=15$$

Subtract 6 from 14 to get 8.

$$-4\times \frac{8}{3}-7y=15$$

Express -4\times \frac{8}{3} as a single fraction.

$$\frac{-4\times 8}{3}-7y=15$$

Multiply -4 and 8 to get -32.

$$\frac{-32}{3}-7y=15$$

Fraction \frac{-32}{3} can be rewritten as -\frac{32}{3} by extracting the negative sign.

$$-\frac{32}{3}-7y=15$$

Add \frac{32}{3} to both sides.

$$-7y=15+\frac{32}{3}$$

Convert 15 to fraction \frac{45}{3}.

$$-7y=\frac{45}{3}+\frac{32}{3}$$

Since \frac{45}{3} and \frac{32}{3} have the same denominator, add them by adding their numerators.

$$-7y=\frac{45+32}{3}$$

Add 45 and 32 to get 77.

$$-7y=\frac{77}{3}$$

Divide both sides by -7.

$$y=\frac{\frac{77}{3}}{-7}$$

Express \frac{\frac{77}{3}}{-7} as a single fraction.

$$y=\frac{77}{3\left(-7\right)}$$

Multiply 3 and -7 to get -21.

$$y=\frac{77}{-21}$$

Reduce the fraction \frac{77}{-21} to lowest terms by extracting and canceling out 7.

$$y=-\frac{11}{3}$$