Mark W. answered • 11/13/14
Tutor
4
(1)
Former Air Force Officer / Certified (SC, TX) HS Math Teacher
I always begin by copying the problem where I am working, then checking to make sure I copied it properly (so many kids make mistakes because the copied it wrong and are working the wrong problem):
-4x -2 ≤ -2x + 8
I will begin by transposing the 4x, so I add 4x to both sides. On the left, it cancels out, but on the right 4x + -2x = 2x:
-2 ≤ 2x + 8
Now, we subtract 8 from both sides; on the right it cancels out:
-10 ≤ 2x
Divide both sides by 2:
-5 ≤ x
To graph this, we draw a solid dot over -5, then an arrow off to the right side, because x may be bigger than -5.
With these signs, ≤ ≥, we use a solid dot, and with < > we use an open circle. The reason is that the solid dot includes the number indicated, while the open circle excludes it.
Also, notice in the problem I was dividing by a positive number. If I divide an inequality by a negative number, it changes the sense of the inequality (we "flip" the sign), but that was not the case here.
I will begin by transposing the 4x, so I add 4x to both sides. On the left, it cancels out, but on the right 4x + -2x = 2x:
-2 ≤ 2x + 8
Now, we subtract 8 from both sides; on the right it cancels out:
-10 ≤ 2x
Divide both sides by 2:
-5 ≤ x
To graph this, we draw a solid dot over -5, then an arrow off to the right side, because x may be bigger than -5.
With these signs, ≤ ≥, we use a solid dot, and with < > we use an open circle. The reason is that the solid dot includes the number indicated, while the open circle excludes it.
Also, notice in the problem I was dividing by a positive number. If I divide an inequality by a negative number, it changes the sense of the inequality (we "flip" the sign), but that was not the case here.
