Solve and graph the solution to the inequality −6n+3≥21. Then explain what the solution means
To solve the inequality −6n+3≥21, we need to isolate the variable n.
Adding -3 to both sides of the inequality, we get:
−6n ≥ 18
Now, dividing both sides by -6, remembering that when we divide or multiply an inequality by a negative number, the inequality sign must be flipped, we have:
n ≤ -3
To graph the solution, we can represent the solution as a number line. Starting from -3, we shade to the left to represent that n can take on any value less than or equal to -3.
In interval notation, the solution can be written as (-∞, -3]. This means that n is a real number that is less than or equal to -3.
The solution means that any number less than or equal to -3 will satisfy the inequality.
as a 6th grade wrote it
To solve the inequality −6n+3≥21, we need to get n by itself on one side of the inequality.
First, we subtract 3 from both sides:
−6n ≥ 18
Next, we divide both sides by -6 (remembering to flip the inequality sign because we are dividing by a negative number):
n ≤ -3
To graph the solution, we need to draw a number line. We put a closed circle on -3 (because it includes -3 in the solution) and draw an arrow going to the left to show that n can be any number less than or equal to -3.
This solution means that any number less than or equal to -3 makes the inequality true.