Solve 4x-(2t-5)=3-4(2t+3)

$$4 x - ( 2 t - 5 ) = 3 - 4 ( 2 t + 3 )$$

Solve for t

$$t=\frac{-2x-7}{3}$$

Steps for Solving Linear Equation

To find the opposite of 2t-5, find the opposite of each term.

$$4x-2t+5=3-4\left(2t+3\right)$$

Use the distributive property to multiply -4 by 2t+3.

$$4x-2t+5=3-8t-12$$

Subtract 12 from 3 to get -9.

$$4x-2t+5=-9-8t$$

Add 8t to both sides.

$$4x-2t+5+8t=-9$$

Combine -2t and 8t to get 6t.

$$4x+6t+5=-9$$

Subtract 4x from both sides.

$$6t+5=-9-4x$$

Subtract 5 from both sides.

$$6t=-9-4x-5$$

Subtract 5 from -9 to get -14.

$$6t=-14-4x$$

The equation is in standard form.

$$6t=-4x-14$$

Divide both sides by 6.

$$\frac{6t}{6}=\frac{-4x-14}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$t=\frac{-4x-14}{6}$$

Divide -14-4x by 6.

$$t=\frac{-2x-7}{3}$$

Solve for x

$$x=\frac{-3t-7}{2}$$

Steps for Solving Linear Equation

To find the opposite of 2t-5, find the opposite of each term.

$$4x-2t+5=3-4\left(2t+3\right)$$

Use the distributive property to multiply -4 by 2t+3.

$$4x-2t+5=3-8t-12$$

Subtract 12 from 3 to get -9.

$$4x-2t+5=-9-8t$$

Add 2t to both sides.

$$4x+5=-9-8t+2t$$

Combine -8t and 2t to get -6t.

$$4x+5=-9-6t$$

Subtract 5 from both sides.

$$4x=-9-6t-5$$

Subtract 5 from -9 to get -14.

$$4x=-14-6t$$

The equation is in standard form.

$$4x=-6t-14$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{-6t-14}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{-6t-14}{4}$$

Divide -14-6t by 4.

$$x=\frac{-3t-7}{2}$$