Given #-2x-5

Question

Given #-2x-5 < -2# I got #-2x < 3#. Is this correct? How do I solve from here?

Savannah Anderson · Accepted Answer

Your answer is not wrong; but it is incomplete.
#color(white)("XXX")-2x-5 < -2color(white)("XX")rarrcolor(white)("XX")color(green)(x > -3/2)# From #color(white)("XXX")-2x-5 < -2# to #color(white)("XXX")-2x < 3#, you were able to arrive. Let's begin there. Isolating a single #x# on one side of the inequality is the aim of "solving" one of these problems. I see two approaches to this: Method 1: Keep in mind the inequality sign reversal rule, which allows you to multiply or divide both sides of an inequality by any negative number. #color(white)("XXX")-2x color(blue)< 3# #color(white)("XXXXX")#becomes #color(white)("XXX")x color(red)( > ) -3/2# after dividing both sides by #(-2)#. Method 2: Keep in mind that you can multiply or divide both sides of an inequality by any number larger than zero, or you can add or subtract the same amount from each side without changing the inequality's orientation. #color(white)("XXX")-2x < 3# #color(white)("XXXXXX")#after adding #2x# to both sides, becomes #color(white)("XXX")0 < 3 +2x# #color(white)("XXXXXX")#then subtracting #3# from both sides, becomes #color(white)("XXX")-3 \ 2x# #color(white)("XXXXXX")#and, ultimately, dividing both sides by #2# #color(white)("XXX")-3/2 < x# #color(white)("XXXXXXXXX")#, which is just another way of writing #x > -3/2#.

Nathan Axel · Answer

#x > -3/2#

#-2x-5<-2#

As a general rule, it's important to keep in mind that if you multiply any of an inequality's sides by a negative number, you must reverse the inequality sign's direction because each side's sign has changed, essentially reflecting the relationship's original origin on the number line.

Thus, when #-1# is multiplied, it becomes:

Color(red)(>) 2# #2x+5

Next, some algebra

#2x+5 - 5 > 2 - 5#

#2x > -3#

And split each side in half:

#x > -3/2#

It takes a little longer to solve if you simply add or subtract the appropriate amounts from each side of the inequality, but here it is.

-5 color(blue)(+ 5) #-2x color(red)(+ 2x) color(blue)(+ 5)

#implies 0< 3 + 2x#

#0 - 3< 3 - 3 + 2x#

#-3< 2x#

Change the sequence:

#2x > - 3#

And split each side in half:

#x > -3/2#

The most crucial part is probably this one: You can always double-check your solution by solving the equality first, adding values to either side of the point where you believe the inequality to emerge, or simply drawing or plotting it.

Abigail Allen · Answer

undefined Yes, your simplification is correct. To solve for $x$, divide both sides of the inequality by $-2$, remembering to reverse the inequality sign because you are dividing by a negative number: $-2x < 3 \Rightarrow x > -\frac{3}{2}$. So, the solution is $x > -\frac{3}{2}$.

Given #-2x-5 &lt; -2# I got #-2x &lt; 3#. Is this correct? How do I solve from here?

Given #-2x-5 < -2# I got #-2x < 3#. Is this correct? How do I solve from here?