Solve this inequality and graph the solution on a number line. Explain what
your solution means in terms of the situation.
To solve an inequality and graph the solution on a number line, let's look at an example:
Let's solve the inequality: 2x + 3 < 7
To solve this inequality, we'll first isolate the variable x.
2x < 7 - 3
2x < 4
Now, divide both sides of the inequality by 2:
x < 4/2
x < 2
This means that x is less than 2.
To graph this solution on a number line, draw a number line and mark a point at 2. Since x is less than 2, we use an open circle to represent 2. Then, draw an arrow to the left indicating that the numbers less than 2 are part of the solution.
So, on the number line, we have an open circle at 2 and an arrow pointing to the left. This visual representation shows us that any number less than 2 is a solution to the inequality.
In terms of the situation, this solution means that any number less than 2 will satisfy the inequality 2x + 3 < 7. For example, if x = 1, then 2(1) + 3 = 5, which is less than 7 and satisfies the inequality.
To properly answer your question, I would need to know the specific inequality that you would like me to solve. Please provide the inequality equation, and I will gladly solve it step-by-step, graph the solution on a number line, and explain the solution in terms of the situation.
To solve an inequality, we need to isolate the variable on one side of the inequality sign.
Let's say the given inequality is:
5x + 2 < 12
To solve this inequality, we need to follow these steps:
Step 1: Subtract 2 from both sides of the inequality:
5x + 2 - 2 < 12 - 2
5x < 10
Step 2: Divide both sides by 5 (since the coefficient of x is 5):
(5x)/5 < 10/5
x < 2
Now, let's graph the solution on a number line.
To graph x < 2, we start by drawing a number line. Then, we plot an open circle at the number 2. Finally, we draw an arrow to the left, indicating that any number less than 2 satisfies the inequality.
Number Line:
-3 -2 -1 0 1 2 3
o------------------------------->
Solution on the Number Line:
-3 -2 -1 0 1 2 3
o------------------------------->
x < 2
This solution means that any value of x that is less than 2 will satisfy the given inequality, which is 5x + 2 < 12. If we substitute any value less than 2 into this inequality, it will be true. For example, if we substitute x = 1, we get 5(1) + 2 = 7, which is indeed less than 12.