Write two inequalities that require that you to use the addition, subtraction, multiplication, and division properties in order to solve them. Solve the inequality you wrote and graph the solutions on a number line
What inequality did you write? We cannot graph here.
Sure! Let's start with the first inequality:
1. 6x + 4 > 14
To solve this inequality, we will use the addition and subtraction properties. We need to isolate the variable 'x' on one side of the inequality. Here's how we do it:
6x + 4 > 14
Subtract 4 from both sides:
6x > 14 - 4
6x > 10
Now divide both sides by 6 to isolate 'x':
(6x)/6 > 10/6
x > 5/3
So the solution to the first inequality is x > 5/3.
Now, let's move on to the second inequality:
2. 3(x - 2) ≤ 9
To solve this inequality, we will use the multiplication and subtraction properties. Again, we need to isolate the variable 'x'. Here's how we do it:
3(x - 2) ≤ 9
Distribute the 3:
3x - 6 ≤ 9
Add 6 to both sides:
3x - 6 + 6 ≤ 9 + 6
3x ≤ 15
Now divide both sides by 3 to isolate 'x':
(3x)/3 ≤ 15/3
x ≤ 5
So the solution to the second inequality is x ≤ 5.
To graph the solutions on a number line, we'll draw a number line and mark the points where the solutions lie. For the first inequality (x > 5/3), we'll draw an open circle at 5/3 and shade all the values greater than it. For the second inequality (x ≤ 5), we'll draw a closed circle at 5 and shade all the values less than or equal to it. Here's the graph:
-------------------------●----->
5/3 5
The filled-in circle at 5 indicates inclusion, while the open circle at 5/3 indicates exclusion.