Solve the inequality. Graph and check your solutions.
1/3 +a < - 2/3
a
To solve the inequality, we need to isolate the variable "a" on one side of the inequality sign.
1/3 + a < -2/3
To do this, we can subtract 1/3 from both sides of the inequality:
1/3 + a - 1/3 < -2/3 - 1/3
On the left side, the 1/3 and -1/3 cancel out, leaving us with just "a":
a < -2/3 - 1/3
Simplifying the right side:
a < -3/3
Since -3/3 is equal to -1, we have:
a < -1
Now, let's graph this inequality on a number line. We will use an open circle at -1 to indicate that this value is not included in the solution set:
-1
--------------------------------
-∞ --------------------------------- ∞
We can see that all values to the left of -1 are solutions to the inequality.
Finally, we can check some values to verify our solution. Let's use a value to the left of -1, a value to the right of -1, and the value -1 itself:
If we choose a = -2, plugging it into the original inequality:
1/3 + (-2) < -2/3
1/3 - 2 < -2/3
-5/3 < -2/3 (which is true)
If we choose a = 0, plugging it into the original inequality:
1/3 + 0 < -2/3
1/3 < -2/3 (which is false)
If we choose a = -1, plugging it into the original inequality:
1/3 + (-1) < -2/3
-2/3 < -2/3 (which is false)
From these checks, we can see that the solution to the inequality is a < -1.