Solve the inequality. Graph the solution set and write it in interval notation.
- 3x <= - 54
Write the answer in interval notation.
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The inequality is -3x <= -54. We can solve it by dividing both sides by -3, making sure to reverse the inequality sign since we are dividing by a negative number:
x >= (-54)/(-3)
Simplifying the right side:
x >= 18
To graph the solution set, we need to plot all the values of x that satisfy the inequality. Since x is greater than or equal to 18, we can represent this on a number line by shading the region to the right of 18 and including 18 itself.
The solution set in interval notation is [18, +∞).
To solve the inequality -3x ≤ -54, we will divide both sides by -3. However, keep in mind that when we multiply or divide an inequality by a negative number, the direction of the inequality sign needs to be reversed.
Dividing both sides by -3, we have:
-3x / -3 ≥ -54 / -3
Simplifying,
x ≥ 18
To graph the solution set, we draw a number line and mark a closed circle at 18 since the inequality is inclusive of that value. Then, we shade the region to the right of 18 to represent all values greater than or equal to 18.
The graph would look like this:
------------●===============================>
In interval notation, we can write the solution set as [18, ∞). This means that x is greater than or equal to 18 and can take any value from 18 to infinity.
To solve the inequality -3x <= -54, we need to isolate the variable x.
First, we'll start by dividing both sides of the inequality by -3. However, when dividing by a negative number, we need to remember that the direction of the inequality symbol must be flipped.
So, dividing both sides of the inequality by -3 yields:
x >= -54 / -3
Simplifying further:
x >= 18
This means that x must be greater than or equal to 18.
Now let's graph the solution set on a number line:
-----------------●----------------
-20 -10 0 10 20 30 40 50 60
Since x is greater than or equal to 18, we'll shade the portion of the number line to the right of 18 and include 18 itself.
-----------------●=======================
-20 -10 0 10 20 30 40 50 60
The shaded portion of the number line represents the solution set.
In interval notation, we write this as [18, ∞). The square bracket on 18 indicates that it is included in the solution set, while the infinity symbol (∞) represents that the numbers continue indefinitely to the right.