choose the correct solution and graph for the inequality 2x-2<-12 or 2x +3>7
To solve the first inequality, 2x - 2 < -12, we can begin by adding 2 to both sides:
2x - 2 + 2 < -12 + 2
This simplifies to:
2x < -10
Next, divide both sides by 2:
(2x)/2 < (-10)/2
Which gives us:
x < -5
For the second inequality, 2x + 3 > 7, we can subtract 3 from both sides:
2x + 3 - 3 > 7 - 3
Simplifying:
2x > 4
Finally, divide both sides of the equation by 2:
(2x)/2 > (4)/2
This results in:
x > 2
Now we can plot these inequalities on a number line:
On the number line, mark an open circle at -5 to represent x < -5.
Next, mark an open circle at 2 to represent x > 2.
Since the first inequality is less than -5, we should shade to the left of -5.
Since the second inequality is greater than 2, we should shade to the right of 2.
The correct graph will show a shaded section to the left of -5 and a shaded section to the right of 2, with open circles at -5 and 2.
Here is the graph:
Number line graph:
-----------•------------•----------
-5 2