# Solutions to linear equations

4 videos

1 skill

Not every linear equation has exactly one solution. Some have no solutions and others might have an infinite number of solutions. This tutorial will give you the intuition on when these different situations arise.

### How to tell if an equation doesn't have a solution

VIDEO
1:55 minutes

An equations with NO solution? Is that possible? In this video, Sal attempts to solve 8(3x + 10) = 28x - 14 - 4x only to find that there isn't a solution.

### How to tell if an equation has one, zero, or infinite solutions

VIDEO
5:28 minutes

Sal shows how some equations have one solution (like -7x + 3 = 2x + 2) and others have no solutions (like -7x + 3 = 2x + 2 - 9x) and still others have infinite solutions (like -7x + 2 = 2x + 2 - 9x).

### How to make an equation with infinitely many solutions (example)

VIDEO
1:40 minutes

Sal shows how to complete the equation 4(x - 2) + x = 5x + __ so that it has infinitely many solutions.

### How to make an equation with no solutions (example)

VIDEO
1:23 minutes

Sal shows how to complete the equation -11x + 4 = __x + __ so that it has no solutions.

### Linear equations with one, zero, or infinite solutions

PRACTICE PROBLEMS

Practice telling whether an equation has one, zero, or infinite solutions.