Solve the inequality. Graph and check your solutions.
1/4>n+4
To solve the inequality 1/4 > n + 4, we can start by isolating the variable n.
1/4 > n + 4
We can start by subtracting 4 from both sides:
1/4 - 4 > n + 4 - 4
-15/4 > n
Next, we can simplify the inequality by finding a common denominator:
-15/4 = -3.75
So, the simplified inequality is:
-3.75 > n
To graph this inequality, we will graph the line n = -3.75 as a dashed line (since the inequality does not include "equal to"). Then, since we want n to be less than -3.75, we shade the region to the left of the line.
Checking the solutions, we can test a value, such as n = -4, to see if it satisfies the inequality:
1/4 > -4 + 4
1/4 > 0
Since 1/4 is indeed greater than 0, n = -4 is a valid solution.
Therefore, the solution to the inequality is n < -3.75.
To solve the inequality 1/4 > n + 4, we first need to isolate the variable n.
Step 1: Subtract 4 from both sides:
1/4 - 4 > n
Step 2: Simplify the left side:
-15/4 > n
Now let's graph the solution on a number line to visualize the values of n that satisfy the inequality.
On the number line, we will represent the value -15/4 as -3.75.
--------o------------------ (number line)
-∞, -3.75]
The solution to the inequality is n ≤ -3.75.
To check our solution, we can substitute a value of n that is less than or equal to -3.75 into the original inequality, and see if it holds true.
For example, let's substitute n = -4 into the inequality:
1/4 > -4 + 4
1/4 > 0
Since 1/4 is indeed greater than 0, our solution is correct.
To solve the inequality 1/4 > n + 4, we'll start by isolating the variable n.
1. Subtract 4 from both sides of the inequality:
1/4 - 4 > n + 4 - 4
-15/4 > n
So, the solution to the inequality is n < -15/4.
Now, let's graph the solution on a number line to visualize all the values of n that satisfy the inequality:
-------------------●
-4 |
● |
● |
● |
● |
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In the graph above, the open circle indicates that -4 is not included in the solution, as the inequality states n is less than, not equal to, -4. All the values to the left of -4 on the number line satisfy the inequality.
To check the solutions, we can substitute some values into the original inequality and see if they hold true.
1. Let's choose n = -5. Substituting it into the original inequality:
1/4 > -5 + 4
1/4 > -1
Since -1 is less than 1/4, this solution holds true.
2. Let's choose n = -3. Substituting it into the original inequality:
1/4 > -3 + 4
1/4 > 1
Since 1 is not less than 1/4, this solution does not hold true.
By following these steps, we solved the inequality, graphed the solution, and checked its validity using sample values.