Solve 1/2x+3/-2x+1=10945

$$\frac { 1 / 2 x + 3 } { - 2 x + 1 } = 10945$$

Solve for x

$$x=\frac{21884}{43781}\approx 0.499851534$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by -2x+1.

$$\frac{1}{2}x+3=10945\left(-2x+1\right)$$

Use the distributive property to multiply 10945 by -2x+1.

$$\frac{1}{2}x+3=-21890x+10945$$

Add 21890x to both sides.

$$\frac{1}{2}x+3+21890x=10945$$

Combine \frac{1}{2}x and 21890x to get \frac{43781}{2}x.

$$\frac{43781}{2}x+3=10945$$

Subtract 3 from both sides.

$$\frac{43781}{2}x=10945-3$$

Subtract 3 from 10945 to get 10942.

$$\frac{43781}{2}x=10942$$

Multiply both sides by \frac{2}{43781}, the reciprocal of \frac{43781}{2}.

$$x=10942\times \frac{2}{43781}$$

Multiply 10942 and \frac{2}{43781} to get \frac{21884}{43781}.

$$x=\frac{21884}{43781}$$