Solve 30w-(-w+6)+(-5w+4)=-(5w+6)t

$$30 w - ( - w + 6 ) + ( - 5 w + 4 ) = - ( 5 w + 6 ) t$$

Solve for t

$$t=\frac{2\left(1-13w\right)}{5w+6}$$

$$w\neq -\frac{6}{5}$$

Steps for Solving Linear Equation

To find the opposite of -w+6, find the opposite of each term.

$$30w-\left(-w\right)-6-5w+4=\left(-\left(5w+6\right)\right)t$$

Combine 30w and -5w to get 25w.

$$25w-\left(-w\right)-6+4=\left(-\left(5w+6\right)\right)t$$

Add -6 and 4 to get -2.

$$25w-\left(-w\right)-2=\left(-\left(5w+6\right)\right)t$$

To find the opposite of 5w+6, find the opposite of each term.

$$25w-\left(-w\right)-2=\left(-5w-6\right)t$$

Use the distributive property to multiply -5w-6 by t.

$$25w-\left(-w\right)-2=-5wt-6t$$

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

$$-5wt-6t=25w-\left(-w\right)-2$$

Multiply -1 and -1 to get 1.

$$-5wt-6t=25w+w-2$$

Combine 25w and w to get 26w.

$$-5wt-6t=26w-2$$

Combine all terms containing t.

$$\left(-5w-6\right)t=26w-2$$

Divide both sides by -5w-6.

$$\frac{\left(-5w-6\right)t}{-5w-6}=\frac{26w-2}{-5w-6}$$

Dividing by -5w-6 undoes the multiplication by -5w-6.

$$t=\frac{26w-2}{-5w-6}$$

Divide 26w-2 by -5w-6.

$$t=-\frac{2\left(13w-1\right)}{5w+6}$$

Solve for w

$$w=-\frac{2\left(3t-1\right)}{5t+26}$$

$$t\neq -\frac{26}{5}$$

Steps for Solving Linear Equation

To find the opposite of -w+6, find the opposite of each term.

$$30w-\left(-w\right)-6-5w+4=\left(-\left(5w+6\right)\right)t$$

Combine 30w and -5w to get 25w.

$$25w-\left(-w\right)-6+4=\left(-\left(5w+6\right)\right)t$$

Add -6 and 4 to get -2.

$$25w-\left(-w\right)-2=\left(-\left(5w+6\right)\right)t$$

To find the opposite of 5w+6, find the opposite of each term.

$$25w-\left(-w\right)-2=\left(-5w-6\right)t$$

Use the distributive property to multiply -5w-6 by t.

$$25w-\left(-w\right)-2=-5wt-6t$$

Add 5wt to both sides.

$$25w-\left(-w\right)-2+5wt=-6t$$

Add 2 to both sides.

$$25w-\left(-w\right)+5wt=-6t+2$$

Multiply -1 and -1 to get 1.

$$25w+w+5wt=-6t+2$$

Combine 25w and w to get 26w.

$$26w+5wt=-6t+2$$

Combine all terms containing w.

$$\left(26+5t\right)w=-6t+2$$

The equation is in standard form.

$$\left(5t+26\right)w=2-6t$$

Divide both sides by 26+5t.

$$\frac{\left(5t+26\right)w}{5t+26}=\frac{2-6t}{5t+26}$$

Dividing by 26+5t undoes the multiplication by 26+5t.

$$w=\frac{2-6t}{5t+26}$$

Divide -6t+2 by 26+5t.

$$w=\frac{2\left(1-3t\right)}{5t+26}$$