Solving linear equations and linear inequalities — Basic example
About this video
Solving the linear inequality 3l - 6 >= 8 means isolating l with inverse operations. The narrator adds 6 to both sides, then divides by 3, and explains that the inequality sign only flips when dividing or multiplying by a negative number.
You'll be able to
- isolate a variable in a linear inequality using inverse operations.
- explain when an inequality sign must stay the same and when it must reverse.
- justify each step of solving a linear inequality.
Key words
- Linear inequality
- A statement comparing a linear expression with a number using <, >, <=, or >=.
- Inverse operation
- An operation that undoes another, such as adding 6 to undo subtracting 6.
- Isolate the variable
- Use inverse operations until the variable stands alone on one side.
- Sign reversal
- The inequality sign flips only when both sides are multiplied or divided by a negative number.
Transcript
- [Instructor] Three l minus six is greater than or equal to eight. Which of the following best describes the solutions to the inequality shown above? So it's three times l minus six is greater than or equal to eight. Well, all of these choices, these are in terms of l.
They said l on one side, and is greater than or equal to, actually all of these choices are greater than or equal to something else. So let's see what we can do to get just an l on the left-hand side. So the first thing we might wanna do, is let's get rid of this subtracting of six.
And the best way we can do that is we can add six. Let's add six to both sides. This six and this six are going to add to zero. And then we are going to be left with, we're going to be left with three l on the left-hand side is greater than or equal to eight plus six is 14.
Now just got an l on the left-hand side. We can divide both sides by three. And if you divide both sides by three, you're not going to change the sign. You're not gonna change the inequality. If you're dividing by a negative number you would swap the inequality.
Greater than or equal to would turn to less than or equal to. But we're dividing by a positive number, so this is going to be l is greater than or equal to 14 over three. Which is that choice right there.
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