Math  /  Algebra

Questionn413n-4 \geq 13

Studdy Solution

STEP 1

1. The inequality n413 n - 4 \geq 13 is asking us to solve for n n .
2. This is a one-step inequality with one solution set.
3. The inequality involves basic algebraic operations, specifically addition.

STEP 2

1. Understand the inequality and what it represents.
2. Isolate the variable n n by performing algebraic operations.
3. Verify the solution by checking a value from the solution set.

STEP 3

The inequality n413 n - 4 \geq 13 indicates that n n minus 4 is greater than or equal to 13. Our goal is to find the values of n n that satisfy this condition.

STEP 4

To isolate n n , we need to eliminate the 4-4 on the left side. We do this by adding 4 to both sides of the inequality:
n4+413+4 n - 4 + 4 \geq 13 + 4

STEP 5

Simplify both sides of the inequality:
n17 n \geq 17
This means that n n must be greater than or equal to 17.

STEP 6

To verify the solution, choose a value for n n that satisfies the inequality. For example, let n=17 n = 17 :
Substitute n=17 n = 17 into the original inequality:
17413 17 - 4 \geq 13

STEP 7

Simplify the left side:
1313 13 \geq 13
This statement is true, confirming that our solution is correct.
Therefore, the solution is:
n17 n \geq 17

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