Algebra 1

To solve an absolute value inequality, get the absolute value alone, then rewrite it. |x| < 3 means −3 < x < 3 (an “and” inequality). |x| > 3 means x < −3 or x > 3 (an “or” inequality).

To solve an absolute value equation, get the absolute value alone, then split it into two equations. For example, |x − 2| = 5 means x − 2 = 5 or x − 2 = −5, so x = 7 or x = −3.

A compound inequality is two inequalities joined by “and” or “or.” An “and” inequality, like −2 < x ≤ 3, is true where both parts are true. An “or” inequality is true where at least one part is true.

A literal equation is an equation with two or more variables, like a formula. To solve it for one variable, get that variable alone with inverse operations. For example, solving d = rt for t gives t = d/r.

To solve equations with variables on both sides, get all the variable terms on one side and all the numbers on the other. For example, 5x + 2 = 3x + 10 becomes 2x + 2 = 10, so x = 4.

A system of two linear equations has one solution, no solution or infinitely many solutions. Lines with different slopes cross once, so there is one solution. Parallel lines never cross, so there is no solution. If both equations make the same line, every point on it is a solution. Before this lesson: You should know…

The substitution method solves a system of equations by replacing one variable with an equal expression. Solve one equation for x or y, then substitute that expression into the other equation and solve. Put that answer back into either equation to find the other variable, and check both. Before this lesson: You should know what…

The elimination method solves a system of equations by adding or subtracting the equations so that one variable cancels out. If nothing cancels right away, first multiply one or both equations so a pair of coefficients become opposites. Solve for the variable that’s left, then substitute to find the other one. Before this lesson: You…

A system of equations is two or more equations that use the same variables. Its solution is the point that makes every equation true at the same time. When you graph a system of two linear equations, the solution is the point where the two lines cross. Before this lesson: You should know how to…

To graph a linear inequality in two variables, graph its boundary line, then shade the side that holds the solutions. Use a solid line for ≤ or ≥ and a dashed line for < or >. To choose a side, test a point such as (0, 0). If it makes the inequality true, shade the…