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Solving Two-Step Linear Equations

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

In the equation 3 x + 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.

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

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

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

3 x 3 = 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 = 3 x + 2 . This equation has not just one but infinitely many solutions; the solutions can be graphed as a line in the plane.