Solve the inequality n minus four sevenths is greater than or equal to negative two thirds for n.
n is greater than or equal to negative 2 over twenty one
n is less than or equal to two over twenty one
n is greater than or equal to negative twenty six over twenty one
n is less than or equal to twenty six over twenty one
To solve the inequality n - 4/7 ≥ -2/3 for n, we can start by getting rid of the fractions.
First, we can multiply both sides of the inequality by 3 to eliminate the fraction -2/3 on the right side:
3(n - 4/7) ≥ -2/3 * 3
This simplifies to:
3n - 12/7 ≥ -6/3
Next, we need to get rid of the fraction 12/7. We can do this by multiplying both sides of the inequality by 7:
7(3n - 12/7) ≥ -6/3 * 7
This simplifies to:
21n - 12 ≥ -14
Now, we can add 12 to both sides of the inequality to get n by itself:
21n - 12 + 12 ≥ -14 + 12
This simplifies to:
21n ≥ -2
Finally, we can divide both sides of the inequality by 21 to solve for n:
n ≥ -2/21
So the solution to the inequality n - 4/7 ≥ -2/3 is n ≥ -2/21.
To solve the inequality n - (4/7) ≥ (-2/3) for n, we can follow these steps:
Step 1: Add (4/7) to both sides of the inequality:
n - (4/7) + (4/7) ≥ (-2/3) + (4/7)
This simplifies the inequality to:
n ≥ (-2/3) + (4/7)
Step 2: Find the least common denominator (LCD) between 3 and 7, which is 21.
Step 3: Convert the fractions to have a denominator of 21:
n ≥ (-2/3) * (7/7) + (4/7) * (3/3)
n ≥ (-14/21) + (12/21)
This simplifies to:
n ≥ (-14 + 12)/21
n ≥ (-2/21)
Therefore, the solution to the inequality n - (4/7) ≥ (-2/3) is:
n ≥ (-2/21)
So, n is greater than or equal to (-2/21).
To solve the inequality, n - 4/7 ≥ -2/3, we'll follow these steps:
Step 1: Add 4/7 to both sides of the inequality:
n - 4/7 + 4/7 ≥ -2/3 + 4/7
n ≥ (-2/3 + 4/7)
Step 2: Find the least common denominator (LCD) of the fractions -2/3 and 4/7, which is 21. Then, rewrite each fraction with that denominator:
n ≥ (-14/21 + 12/21)
Step 3: Simplify the right side of the inequality:
n ≥ -2/21
Thus, the correct answer is:
n is greater than or equal to -2/21.