Solving Two-Step Linear Equations
More commonly, we need two operations to solve a linear equations.
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 . . . . . . . – 5 . . . . subtract 5 from each side to get constants on the right
3x = 6 . . . . . . . . . . . the result
3x /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 x1 (no x2 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.
