Section 5

Solving linear equations with one variable and one equation

To solve a linear equation with one variable, move the unknown variable to the left-hand side of the equal sign. Move all the other terms to the right-hand side of the equal sign. Then simplify both sides of the equation until you get only the unknown variable in the left with coefficient 1, then the term in the right-side of the equal sign is the solution.

For example, see how to solve the following linear equation:

$$5x + 10 = 8x - 5$$

Move all terms with the unknown variable \(x\) to the left:

$$5x + 10 - 8x = -5$$

Move any term without the unknown to the right: $$5x - 8x = -5 - 10$$ Simplify both sides of the equation until you get only the unknown variable in the left with coefficient \(1\): $$-3x = -15$$ $$x = 5$$