# Solving basic equations & inequalities (one variable, linear)

Contents

This topic covers:
- Solving one-variable linear equations
- Solving one-variable linear inequalities

23 exercises available

Explore what it means for equations with variables (algebraic equations) to be solved.

A high-level, conceptual walk-through of what an equation represents and why we do the same thing to both sides of it

Solve equations by adding and subtracting numbers from both sides.

Solve equations by multiplying and dividing numbers from both sides.

Learn how to solve equations like 2x+7=13 and 3(x+4)=3, which can be solved in two steps.

Learn how to set up and solve equations to find answers to real-world questions.

Learn how to solve linear equations that have the variable on both sides of the equation. For example, solve 2x+5=6x-3.

Learn how to solve linear equations with parentheses using the distributive property. For example, solve -9 - (9x - 6) = 3(4x + 6).

Linear equations can either have a single solution, infinite solutions, or no solutions. Learn how to determine the number of solutions to a given equation, and how to create equations with a desired number of solutions.

Solve word problems by creating linear equations and solving them.

An equation like ax+3x=bx+5 can still be solved for x even though some of the coefficients are variables.

Some of Sal's oldest (and roughest) videos on algebra. Great tutorial if you want to see what Khan Academy was like around 2006. You might also like it if you feel like Sal has lost his magic now that he doesn't use the cheapest possible equipment to make the videos.

Algebraic inequalities (inequalities with variables) are useful for describing real-world situations. Learn how to write inequalities and graph them on the number line.

Learn how to solve (mathematical) inequalities. A key concept in this tutorial is flipping the inequality sign when multiplying or dividing both sides by a negative number.

Learn how to solve more complex (mathematical) inequalities. Also learn to construct inequalities to model real-world situations.

Solve any possible linear inequality in one variable. For example, solve -3x-7<x+9.

Learn how to solve compound inequalities. For example, solve 2x+1>3 AND -x-5<4.