Edwin_R said:
i can still do it my way right ? I'm not sure; I do not understand your reasoning (see below).
because you said that i will still get the same answer No. What I said is that MY result matches yours; I never said that you would get the same.
can you give me a problem like that and ill solve it please Sure. I'll post it below.
You were given the following inequality to solve for x.
4/3 x + 5 < 17
For
your first step, you typed the following.
(3) 3/4 x + 5 < 17
Why did you change 4/3 to 3/4 ?
Why did you multiply the lefthand side by 3 without multiplying the righthand side by 3 ?
After reading your second step, I stopped reading bacause I can't understand it and I'm too lazy to try figure out what's in your head.
As I said before, solving a simple inequality like this is exactly the same as solving the corresponding equation. You know how to solve equations, yes?
4/3 x + 5 = 17
Subtract 5 from both sides, then multiply both sides by the reciprocal 3/4.
The only difference, when solving these simple inequalities, is that
we must remember the following rule:
When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality symbol must be reversed.
Here's an example why.
-1 is less than 1, right?
-1 < 1
If we multiply both sides by -2 and do NOT reverse the less-than sign, we would have the following.
2 < -2
That inequality is NOT true.
We need to reverse the direction of the inequality symbol, because we multiplied both sides by a negative number.
2 > -2
Here's another example.
100 > 50
You know that's true. Now, divide both sides by -5.
100/(-5) > 50/(-5)
-20 > -10
That result is NOT correct. (-20 is LESS than -10 because -20 lies to the left of -10 on the Real number line, right?)
The result is not correct because I did not reverse the greater-than sign, when dividing both sides by a negative number.
-20 < -10 is true.
Okay, you asked for another inequality to solve, for practice. Here ya go, times two:
\(\displaystyle \frac{3}{8} x \;+\; \frac{7}{8} \;>\; 1\)
and
\(\displaystyle -7 \;-\; (-2x) \;<\; 3\)