Solve for xx and graph the solution on the number line below.
minus, 3, is greater than or equal to, start fraction, x, divided by, minus, 2, end fraction
−3≥
−2
x
To solve for x, we can multiply both sides of the inequality by -2. However, since we are multiplying by a negative number, the inequality sign will flip.
-3 >= (x / -2)
When we multiply both sides by -2, we get:
-3 * -2 <= x
6 <= x
The solution to the inequality is x >= 6.
To graph this solution on the number line, we start at the number 6 and shade everything to the right, including 6.
Number line:
-------------|---|---|---|---|---|---|---|---|---|
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Solution:
-------------|---|---|---|---|---|---|===|===|===|
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10