Solve 1/2x-1*1/3(2x+5)=1

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

Solve for x

$$x=2$$

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 3\left(2x-1\right), the least common multiple of 2x-1,3.

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

Multiply 3 and 1 to get 3.

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

Multiply 3 and \frac{1}{3} to get 1.

$$2x+5=3\left(2x-1\right)$$

Use the distributive property to multiply 3 by 2x-1.

$$2x+5=6x-3$$

Subtract 6x from both sides.

$$2x+5-6x=-3$$

Combine 2x and -6x to get -4x.

$$-4x+5=-3$$

Subtract 5 from both sides.

$$-4x=-3-5$$

Subtract 5 from -3 to get -8.

$$-4x=-8$$

Divide both sides by -4.

$$x=\frac{-8}{-4}$$

Divide -8 by -4 to get 2.

$$x=2$$