Solve 5left(-5z/6-13/6right)+3left(2z/13+49/13right)+4z=-1

$$5 \left( - \frac{ 5z }{ 6 } - \frac{ 13 }{ 6 } \right) +3 \left( \frac{ 2z }{ 13 } + \frac{ 49 }{ 13 } \right) +4z = -1$$

Solve for z

$$z=-5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 78, the least common multiple of 6,13.

$$390\left(-\frac{5z}{6}-\frac{13}{6}\right)+234\left(\frac{2z}{13}+\frac{49}{13}\right)+312z=-78$$

Since -\frac{5z}{6} and \frac{13}{6} have the same denominator, subtract them by subtracting their numerators.

$$390\times \frac{-5z-13}{6}+234\left(\frac{2z}{13}+\frac{49}{13}\right)+312z=-78$$

Cancel out 6, the greatest common factor in 390 and 6.

$$65\left(-5z-13\right)+234\left(\frac{2z}{13}+\frac{49}{13}\right)+312z=-78$$

Use the distributive property to multiply 65 by -5z-13.

$$-325z-845+234\left(\frac{2z}{13}+\frac{49}{13}\right)+312z=-78$$

Since \frac{2z}{13} and \frac{49}{13} have the same denominator, add them by adding their numerators.

$$-325z-845+234\times \frac{2z+49}{13}+312z=-78$$

Cancel out 13, the greatest common factor in 234 and 13.

$$-325z-845+18\left(2z+49\right)+312z=-78$$

Use the distributive property to multiply 18 by 2z+49.

$$-325z-845+36z+882+312z=-78$$

Combine -325z and 36z to get -289z.

$$-289z-845+882+312z=-78$$

Add -845 and 882 to get 37.

$$-289z+37+312z=-78$$

Combine -289z and 312z to get 23z.

$$23z+37=-78$$

Subtract 37 from both sides.

$$23z=-78-37$$

Subtract 37 from -78 to get -115.

$$23z=-115$$

Divide both sides by 23.

$$z=\frac{-115}{23}$$

Divide -115 by 23 to get -5.

$$z=-5$$