Solve the inequality -2 <3x -5 < 7. Graph the solution set.
-2 <3x -5 < 7 now add 5 to each component
3 < 3x < 12 divide by 3
1 < x < 4
so x lies between 1 and 4
on a number line, make open circles at 1 and 4, draw a solid line between these two circles.
To solve the inequality -2 < 3x - 5 < 7, we need to find the values of x that satisfy the given inequality.
First, let's isolate the variable x. We'll add 5 to all parts of the inequality:
-2 + 5 < 3x < 7 + 5
This simplifies to:
3 < 3x < 12
Now, divide all parts of the inequality by 3:
3/3 < 3x/3 < 12/3
This gives us:
1 < x < 4
So the solution set for the inequality is x > 1 and x < 4.
To graph the solution set, we plot an open circle at x = 1 and x = 4 on the number line, and shade the region between these two points since they are both less than and greater than x.