Hello all, thanks you for coming again :) Now I'm going to teach you the topic about linear inequalities. But, before that, did you know the meaning of linear inequalities??
Okey~ Now i'am going to tell what is mean by linear inequalities..
What is linear inequalities?
At Wikipedia said that In mathematics a linear inequality is an Inequalities which involves a linear function. A linear inequality contains one of the symbols of inequality:
- < is less than
- > is greater than
- ≤ is less than or equal to
- ≥ is greater than or equal to
- ≠ is not equal to
A linear inequality looks exactly like a linear equation, with the inequality sign replacing the equality sign.
Solving linear inequalities is almost exactly like solving linear equations.
1) Solve x + 3 < 0.
If they'd given me "x + 3 = 0", I'd have known how to solve: I would have subtracted 3 from both sides. I can do the same thing here:
So the answer is x < –3
2) Solve x - 3 ≤ 2
Step 1
Make "x" become single. mean..we move "- 3" to the back of "2"
Note : If we move "-" to the back, we must change the sign into "+" first!
x ≤ 2 + 3
Step 2
We add 2 and 3. The answer is 5
So, the answer is x ≤ 5
3) Solve 3(x+5) ≤ 2(x+1)
As you can see, this question is different from another question. Here, I will show you step by step.
Step 1
We open bracket first. We multiply 3 into X and 5 and multiply 2 into x and 1
3x(x) + 3x(5) ≤ 2x(x) + 2x(1)
3x + 15 ≤ 2x + 2
Step 2
Then, we make "x" become one.We move +15 into 2x and then we move 2x into +15.
3x(x) + 3x(5) ≤ 2x(x) + 2x(1)
Note: When we move + 15 to anther side, we must change the sign of "+" into "-" .
3x + 15 ≤ 2x + 2
3x - 2x ≤ -5 + 2
Then, we "-" 3x - 2x and "+" -5 + 2
3x - 2x = x
-5 + 2 = -13
So, the answer is x ≤ -13
Working :
3(x+5) ≤ 2(x+1)
3x(x) + 3x(5) ≤ 2x(x) + 2x(1)
3x + 15 ≤ 2x + 2
3x - 2x ≤ -5 + 2
x ≤ -13
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