Solve 3(4x+5)=2(4x-61/2)

$$3 ( 4 x + 5 ) = 2 ( 4 x - 6 \frac { 1 } { 2 } )$$

Solve for x

$$x=-7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$6\left(4x+5\right)=4\left(4x-\frac{6\times 2+1}{2}\right)$$

Use the distributive property to multiply 6 by 4x+5.

$$24x+30=4\left(4x-\frac{6\times 2+1}{2}\right)$$

Multiply 6 and 2 to get 12.

$$24x+30=4\left(4x-\frac{12+1}{2}\right)$$

Add 12 and 1 to get 13.

$$24x+30=4\left(4x-\frac{13}{2}\right)$$

Use the distributive property to multiply 4 by 4x-\frac{13}{2}.

$$24x+30=16x+4\left(-\frac{13}{2}\right)$$

Express 4\left(-\frac{13}{2}\right) as a single fraction.

$$24x+30=16x+\frac{4\left(-13\right)}{2}$$

Multiply 4 and -13 to get -52.

$$24x+30=16x+\frac{-52}{2}$$

Divide -52 by 2 to get -26.

$$24x+30=16x-26$$

Subtract 16x from both sides.

$$24x+30-16x=-26$$

Combine 24x and -16x to get 8x.

$$8x+30=-26$$

Subtract 30 from both sides.

$$8x=-26-30$$

Subtract 30 from -26 to get -56.

$$8x=-56$$

Divide both sides by 8.

$$x=\frac{-56}{8}$$

Divide -56 by 8 to get -7.

$$x=-7$$