# Solving Two-Step Linear Equations

More commonly, we need two operations to solve a linear equation .

In the equation $3x+5=11$ , $x$ is multiplied by $3$ and then $5$ is added. To solve two-step equations, use inverse operations to undo each operation in reverse order.

$3x+5=11$ . . . . . . . our given equation

$-5$ . . . . . . . . . . . . subtract $5$ from each side to get constants on the right

$3x=6$ . . . . . . . . . . . the result

$\frac{3x}{3}=\frac{6}{3}$ . . . . . . . .divide both sides by $3$ to isolate the $x$

$x=2$ . . . . . . . . . . . . the solution (same as before!)

. . . . . . . . . . . . . . . . .We've solved the equation .

The thing that makes these equations linear is that the highest power of $x$ is ${x}^{1}$ (no ${x}^{2}$ or other powers; for those, see quadratic equations and polynomials .

Other linear equations have more than one variable: for example, $y=3x+2$ . This equation has not just one but infinitely many solutions; the solutions can be graphed as a line in the plane.