Solve (2a-1)x+3=5x-2

$$( 2 a - 1 ) x + 3 = 5 x - 2$$

Solve for a

$$a=3-\frac{5}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

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

Add x to both sides.

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

Combine 5x and x to get 6x.

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

Subtract 3 from both sides.

$$2ax=6x-2-3$$

Subtract 3 from -2 to get -5.

$$2ax=6x-5$$

The equation is in standard form.

$$2xa=6x-5$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{6x-5}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{6x-5}{2x}$$

Divide 6x-5 by 2x.

$$a=3-\frac{5}{2x}$$

Solve for x

$$x=-\frac{5}{2\left(a-3\right)}$$

$$a\neq 3$$

Steps for Solving Linear Equation

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

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

Subtract 5x from both sides.

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

Combine -x and -5x to get -6x.

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

Subtract 3 from both sides.

$$2ax-6x=-2-3$$

Subtract 3 from -2 to get -5.

$$2ax-6x=-5$$

Combine all terms containing x.

$$\left(2a-6\right)x=-5$$

Divide both sides by 2a-6.

$$\frac{\left(2a-6\right)x}{2a-6}=-\frac{5}{2a-6}$$

Dividing by 2a-6 undoes the multiplication by 2a-6.

$$x=-\frac{5}{2a-6}$$

Divide -5 by 2a-6.

$$x=-\frac{5}{2\left(a-3\right)}$$