How do you solve the inequality: #4> -5x+3# and #11<-5x+4#?

Answer 1

From the above you meant #4> -5x+3# ?
Let's do them separately

(1) #4> -5x+3->-5x+3<4# subtract 3 and then divide by 5: #-5x< 1->-x<1/5# Now we have to flip all the signs including the inequality-sign: #->x> -1/5#

(2) #11<-5x+4->-5x+4>11# subtract 4 and divide by 5: #->-5x>7->-x>7/5 # Now we have to flip the signs again: #->x<-7/5#

Combining these (as we have to with an AND-question), we get no overlap, so no solution.

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Answer 2

Jace Anderson

To solve the inequality \(4 > -5x + 3\) and \(11 < -5x + 4\): 1. Solve each inequality separately to find the value of \(x\). 2. For \(4 > -5x + 3\), subtract 3 from both sides to get \(1 > -5x\). Then, divide both sides by -5, remembering to flip the inequality sign because of dividing by a negative number, resulting in \(x > -\frac{1}{5}\). 3. For \(11 < -5x + 4\), subtract 4 from both sides to get \(7 < -5x\). Then, divide both sides by -5, remembering to flip the inequality sign, resulting in \(x > -\frac{7}{5}\). 4. Combine the solutions from both inequalities to find the intersection, which is \(x > -\frac{7}{5}\).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve the inequality: #4&gt; -5x+3# and #11&lt;-5x+4#?

How do you solve the inequality: #4> -5x+3# and #11<-5x+4#?