Solve -4/(2-7x)=3-5(1/2)

$$\frac { - 4 } { ( 2 - 7 x ) } = 3 - 5 ( \frac { 1 } { 2 } )$$

Solve for x

$$x = \frac{10}{7} = 1\frac{3}{7} \approx 1.428571429$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{2}{7} since division by zero is not defined. Multiply both sides of the equation by 2\left(7x-2\right), the least common multiple of 2-7x,2.

$$-2\left(-4\right)=2\left(7x-2\right)\times 3-5\times \frac{1}{2}\times 2\left(7x-2\right)$$

Multiply -2 and -4 to get 8.

$$8=2\left(7x-2\right)\times 3-5\times \frac{1}{2}\times 2\left(7x-2\right)$$

Multiply 2 and 3 to get 6.

$$8=6\left(7x-2\right)-5\times \frac{1}{2}\times 2\left(7x-2\right)$$

Use the distributive property to multiply 6 by 7x-2.

$$8=42x-12-5\times \frac{1}{2}\times 2\left(7x-2\right)$$

Multiply 5 and \frac{1}{2} to get \frac{5}{2}.

$$8=42x-12-\frac{5}{2}\times 2\left(7x-2\right)$$

Multiply \frac{5}{2} and 2 to get 5.

$$8=42x-12-5\left(7x-2\right)$$

Use the distributive property to multiply -5 by 7x-2.

$$8=42x-12-35x+10$$

Combine 42x and -35x to get 7x.

$$8=7x-12+10$$

Add -12 and 10 to get -2.

$$8=7x-2$$

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

$$7x-2=8$$

Add 2 to both sides.

$$7x=8+2$$

Add 8 and 2 to get 10.

$$7x=10$$

Divide both sides by 7.

$$x=\frac{10}{7}$$