Solve and graph the inequality.

4/5x + 5

Question

Solve and graph the inequality. 

4/5x + 5 < -3

yanasidlinskiy · Answer

This is what I have done so far: $$\frac{ 4 }{ 5 }x +5 < -3$$
I subtracted 5 from both sides and I'm left with $$\frac{ 4 }{ 5 }x < -8$$
Now i don't know what to do next.

yanasidlinskiy · Answer

@mathmale

mathmale · Answer

Hello, Yana!!
What I'd do here would be to multiply both left and right side of this inequality by (5/4).  This will, in effect, "solve" the inequality for x.  Try doing that, please.

yanasidlinskiy · Answer

I don't really get this. Would it be -15/-12??

mathmale · Answer

Please simplify this.  Think:  What is your goal here?  You need to end up with an inequality involving x.

mathmale · Answer

$$\frac{ 4 }{ 5 }x < -8 \rightarrow (\frac{ 5 }{ 4 })\frac{ 4x }{ 5 }<(\frac{ 5 }{ 4 })(-8)$$

yanasidlinskiy · Answer

Oh...Ok...I got it now. I actually started doing that from the original problem. Would it be $$x \ge -10$$

yanasidlinskiy · Answer

No. It would be $$x < -10$$ right??

yanasidlinskiy · Answer

@mathmale  Am I right?

whpalmer4 · Answer

$$\frac{4}{5}x < -8$$$$(\frac{5}{4})\frac{4}{5}x < (\frac{5}{4})(-8)$$$$\cancel{(\frac{5}{4})\frac{4}{5}}x < (\frac{-40}{4})$$$$x< -10$$

Remember that if you multiply or divide an inequality by a negative number, you have to change the direction of the inequality sign.  It didn't happen here, but it's important to remember that!