Choose the correct solution and graph for the inequality
(3y-6)/3+4<-2 or
(3y-6)/3+4>-2
To solve this inequality, we will first simplify the left side of the equation.
(3y-6)/3+4>-2
(3y-6)/3>-6
Next, we will multiply both sides of the equation by 3 to clear the fraction.
3(3y-6)/3 > -6 * 3
3y-6 > -18
Now, we can add 6 to both sides of the equation to isolate the variable y.
3y-6+6 > -18+6
3y > -12
Finally, we divide both sides of the equation by 3 to solve for y.
3y/3 > -12/3
y > -4
Therefore, the solution to the inequality is y > -4.
Now let's graph the solution on a number line.
On the number line, we mark a point at -4 and draw an arrow to the right to represent all values of y that are greater than -4.
-4→→→→→→
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
The shaded region to the right of -4 represents the solution to the inequality y > -4.