Question $n-4 \geq 13$

Studdy Solution

STEP 1

1. The inequality $n - 4 \geq 13$ is asking us to solve for $n$ .
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.
2. Isolate the variable $n$ by performing algebraic operations.
3. Verify the solution by checking if the inequality holds.

STEP 3

The inequality $n - 4 \geq 13$ is saying that when 4 is subtracted from $n$ , the result is at least 13.

STEP 4

To isolate $n$ , we need to perform the opposite operation of subtraction, which is addition. Add 4 to both sides of the inequality:
$n - 4 + 4 \geq 13 + 4$

STEP 5

Simplify both sides of the inequality:
$n \geq 17$

STEP 6

Verify the solution by checking if the inequality holds for $n = 17$ and any value greater than 17.
For $n = 17$ :
$17 - 4 \geq 13$
$13 \geq 13$
This is true.

STEP 7

For any $n > 17$ , say $n = 18$ :
$18 - 4 \geq 13$
$14 \geq 13$
This is also true.
Therefore, the solution set is:
$n \geq 17$

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