One-step inequality involving addition
About this video
The video solves the inequality x + 8 <= 6 by subtracting 8 from both sides to get x <= -2. It graphs the solution on a number line with a filled-in dot at -2 and shading to the left, then checks the answer by testing -3 (works) and -1 (does not work).
You'll be able to
- solve a one-step inequality by subtracting the same number from both sides.
- graph a 'less than or equal to' solution using a filled-in dot and shading.
- check a solution by testing numbers inside and outside the solution set.
Key words
- inequality
- A maths statement that compares two sides using signs like <, >, <= or >= instead of =.
- isolate the variable
- Get x on its own on one side so you can read off the solution.
- number line
- A line with numbers marked in order, used to show which values are in the solution.
- closed (filled-in) dot
- A solid dot on a number line showing that the number itself is included in the solution.
- open dot
- A hollow circle on a number line showing that the number itself is not included.
Transcript
Solve for x plus 8 is less than or equal to 6 and graph the solution. So we have x plus 8 is less than or equal to 6. So let's solve this inequality for x. And the easiest way to isolate an x on-- let's isolate on the left-hand side since it's already there-- is to just get rid of this 8.
And the best way to get rid of this positive 8 is to subtract 8 from both sides So let's subtract 8 from both sides. That won't change the direction of the inequality. So the left-hand side-- x plus 8 minus 8. And you're just left with an x. The right-hand side-- 6 minus 8 is negative 2.
And we still have the less than or equal. So we solved the inequality. We have x is less than or equal to negative 2. So let's draw that on a number line. So that's my number line. Let's stick 0 over here. Maybe if we go 1, and then we could go negative 1, negative 2, negative 3.
And we could keep going to the left. And we want all of the x's that are less than or equal to negative 2. Since it can be equal to negative 2, we'll put a filled-in line right here at negative 2, and all of the values less than that. If it was just less than, if there wasn't the equal sign, we would have an open dot.
But since this is less than or equal to, we've closed this dot. And then we want all of the values below that. And you could just sample a few and verify for yourself that they work. Based on this, negative 3 should work. And if you took negative 3-- negative 3 plus 8 is 5, which is definitely less than 6, so that works.
And negative 1 shouldn't work. It's not included in this set over here. So let's try that out. Negative 1 plus 8 is 7, which is definitely not less than 6. So just sampling some points, it seems like we've got the right solution.
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