Solve -5/6t-30-1/42=-2/2t-10

$$\frac { - 5 } { 6 t - 30 } - \frac { 1 } { 42 } = \frac { - 2 } { 2 t - 10 }$$

Solve for t

$$t=12$$

Steps for Solving Linear Equation

Variable t cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by 42\left(t-5\right), the least common multiple of 6t-30,42,2t-10.

$$7\left(-5\right)+42\left(t-5\right)\left(-\frac{1}{42}\right)=21\left(-2\right)$$

Multiply 7 and -5 to get -35.

$$-35+42\left(t-5\right)\left(-\frac{1}{42}\right)=21\left(-2\right)$$

Multiply 42 and -\frac{1}{42} to get -1.

$$-35-\left(t-5\right)=21\left(-2\right)$$

To find the opposite of t-5, find the opposite of each term.

$$-35-t+5=21\left(-2\right)$$

Add -35 and 5 to get -30.

$$-30-t=21\left(-2\right)$$

Multiply 21 and -2 to get -42.

$$-30-t=-42$$

Add 30 to both sides.

$$-t=-42+30$$

Add -42 and 30 to get -12.

$$-t=-12$$

Multiply both sides by -1.

$$t=12$$