Question

when we solve an inequality and divide by a negative what do you do with the inequality sign?

Answer 1

-3x > 6 divide both sides by -3 so what will get ?

@XioGonz

Answer 2

a negative?

Answer 3

\[-3x > 6\]
\[\frac{ -3x }{ 3 }>\frac{ 6 }{ 3 }\]
\[x<-2\]

Answer 4

\(\color{#0cbb34}{\text{Originally Posted by}}\) @XioGonz
\[-3x > 6\]
\[\frac{ -3x }{ 3 }>\frac{ 6 }{ 3 }\]
\[x<-2\]
\(\color{#0cbb34}{\text{End of Quote}}\)
divide by minus 3 not plus 3

Answer 5

See how the sign was flipped?

Answer 6

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jhonyy9
\(\color{#0cbb34}{\text{Originally Posted by}}\) @XioGonz
\[-3x > 6\]
\[\frac{ -3x }{ -3 }>\frac{ 6 }{ -3 }\]
\[x<-2\]
\(\color{#0cbb34}{\text{End of Quote}}\)
divide by minus 3 not plus 3
\(\color{#0cbb34}{\text{End of Quote}}\)
My bad Let me correct

Answer 7

There

Answer 8

yeah i was about to say that the sign would flip

Answer 9

i still dont understand

Answer 10

Using @jhonyy9 's example, we can solve for x without dividing both sides by a negative number.

To do this, we need to add 3x to both sides so that the -3 becomes positive.
-3x > 6
-3x+3x > 6+3x
0x > 3x+6
0 > 3x+6

Then next, we subtract 6 from both sides.
0 > 3x+6
0-6 > 3x+6-6
-6 > 3x

To isolate x fully, you need to divide both sides by 3 to undo the multiplication.
-6 > 3x
-6/3 > 3x/3
-2 > x

So -2 is larger than x, which is the same as saying x is smaller than -2
In other words, -2 > x becomes x < -2

Side note: Dividing both sides by a positive number won't flip the inequality sign.

Answer 11

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jimthompson5910
Using @jhonyy9 's example, we can solve for x without dividing both sides by a negative number.

To do this, we need to add 3x to both sides so that the -3 becomes positive.
-3x > 6
-3x+3x > 6+3x
0x > 3x+6
0 > 3x+6

Then next, we subtract 6 from both sides.
0 > 3x+6
0-6 > 3x+6-6
-6 > 3x

To isolate x fully, you need to divide both sides by 3 to undo the multiplication.
-6 > 3x
-6/3 > 3x/3
-2 > x

So -2 is larger than x, which is the same as saying x is smaller than -2
In other words, -2 > x becomes x < -2

Side note: Dividing both sides by a positive number won't flip the inequality sign.
\(\color{#0cbb34}{\text{End of Quote}}\)
oh ok thank you

Answer 12

No problem