Use the multiplication property of inequalities to solve the inequality. Graph the solution set
-1/9t≥2
The solution set is?
t≤-18
To solve the inequality -1/9t ≥ 2 using the multiplication property of inequalities, we first need to isolate the variable t by multiplying both sides of the inequality by -9 (to simplify the equation). However, when we multiply an inequality by a negative number, the direction of the inequality sign is reversed. Therefore, when we multiply both sides of the inequality by -9, we need to remember to switch the direction of the inequality sign.
Let's work through the steps:
-1/9t ≥ 2
Multiply both sides of the inequality by -9:
(-1/9t)(-9) ≤ 2(-9)
This simplifies to:
t ≤ -18
Now we have obtained the solution for t. The solution set for the inequality -1/9t ≥ 2 is t ≤ -18.
To graph the solution set, we represent the solution set on a number line. We start at -18 on the number line and shade all the values to the left, as the inequality is inclusive of -18.
On the number line, we mark -18 with an open circle (since it is not included in the solution set) and shade the line to the left of -18. This represents all the values of t that satisfy the inequality -1/9t ≥ 2.
Graphically, it would look something like this:
o---------------------->
-∞ -18
The shaded portion represents the solution set, which includes all values of t less than or equal to -18.