To solve the inequality [tex]\( x - 3 \geq 7 \)[/tex], follow these steps:
1. Isolate the variable (x):
- We need to get [tex]\( x \)[/tex] by itself on one side of the inequality. To do so, we can eliminate the constant term on the same side as [tex]\( x \)[/tex]. The given inequality is [tex]\( x - 3 \geq 7 \)[/tex].
2. Add 3 to both sides of the inequality:
- To eliminate the [tex]\(-3\)[/tex] from the left side, add 3 to both sides.
[tex]\[
x - 3 + 3 \geq 7 + 3
\][/tex]
3. Simplify the resulting inequality:
- Simplifying each side gives:
[tex]\[
x \geq 10
\][/tex]
The solution to the inequality [tex]\( x - 3 \geq 7 \)[/tex] is [tex]\( x \geq 10 \)[/tex]. In other words, [tex]\( x \)[/tex] must be greater than or equal to 10.
