Solve 14(2t-3)-2(t+2)=10(3t-4)

$$14 ( 2 t - 3 ) - 2 ( t + 2 ) = 10 ( 3 t - 4 )$$

Solve for t

$$t = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 14 by 2t-3.

$$28t-42-2\left(t+2\right)=10\left(3t-4\right)$$

Use the distributive property to multiply -2 by t+2.

$$28t-42-2t-4=10\left(3t-4\right)$$

Combine 28t and -2t to get 26t.

$$26t-42-4=10\left(3t-4\right)$$

Subtract 4 from -42 to get -46.

$$26t-46=10\left(3t-4\right)$$

Use the distributive property to multiply 10 by 3t-4.

$$26t-46=30t-40$$

Subtract 30t from both sides.

$$26t-46-30t=-40$$

Combine 26t and -30t to get -4t.

$$-4t-46=-40$$

Add 46 to both sides.

$$-4t=-40+46$$

Add -40 and 46 to get 6.

$$-4t=6$$

Divide both sides by -4.

$$t=\frac{6}{-4}$$

Reduce the fraction \frac{6}{-4} to lowest terms by extracting and canceling out 2.

$$t=-\frac{3}{2}$$