Algebra 1 Essentials in 3 Minutes

Transcript

If you can solve an equation, read a slope, and handle an inequality, you can handle almost everything Algebra 1 throws at you. These three skills show up on every quiz, every test, and every math class you take after this one. Let's lock them in.

First, solving equations. The whole game is doing the same thing to both sides until the variable stands alone. Say you have three x plus seven equals twenty-two. Subtract seven from both sides, and you get three x equals fifteen. Divide both sides by three, and x equals five. If there are variables on both sides, collect them on one side first, then finish the same way. Every step is legal as long as you do it to both sides.

Second, slope-intercept form. A line written as y equals m x plus b tells you two things instantly: m is the slope, and b is where the line crosses the y axis. So in y equals negative two x plus nine, the slope is negative two and the y intercept is nine. Slope means rise over run — a slope of negative two says that every time you move one step to the right, the line drops two steps down. If you need to write an equation from a point and a slope, plug the point and the slope into y equals m x plus b and solve for b.

Third, inequalities. You solve them exactly like equations, with one famous exception: when you multiply or divide both sides by a negative number, you must flip the inequality sign. Take five x minus three is less than twelve. Add three to both sides to get five x is less than fifteen, then divide by five, a positive number, so the sign stays put: x is less than three.

Now the mistake that costs the most points: forgetting to flip that sign. If you divide both sides of negative two x is less than ten by negative two, the answer is x is greater than negative five — greater than, because you divided by a negative. Students who forget this get the exact opposite of the right answer.

Here's your recap. Solve equations by undoing operations on both sides until the variable is alone, read slope and intercept straight out of y equals m x plus b, and treat inequalities like equations — flipping the sign only when you multiply or divide by a negative. Nail those three moves and you're ready for the practice quiz.