To solve these inequalities and find a pattern, let's examine each of them step by step.
#### 1. Solve [tex]\( x + 1 > 10 \)[/tex]
- Subtract 1 from both sides:
[tex]\[
x + 1 - 1 > 10 - 1 \implies x > 9
\][/tex]
#### 2. Solve [tex]\( x + 11 > 20 \)[/tex]
- Subtract 11 from both sides:
[tex]\[
x + 11 - 11 > 20 - 11 \implies x > 9
\][/tex]
#### 3. Solve [tex]\( x + 21 > 30 \)[/tex]
- Subtract 21 from both sides:
[tex]\[
x + 21 - 21 > 30 - 21 \implies x > 9
\][/tex]
From these three steps, we notice a pattern: regardless of the constant term added to [tex]\( x \)[/tex] on the left-hand side of the inequality, the solution simplifies to [tex]\( x > 9 \)[/tex].
#### Now using the pattern:
Using this observed pattern, we can predict the solution of the next inequality:
#### Solve [tex]\( x + 9,991 > 10,000 \)[/tex]
- Subtract 9,991 from both sides:
[tex]\[
x + 9,991 - 9,991 > 10,000 - 9,991 \implies x > 9
\][/tex]
Thus, the solution to the inequality [tex]\( x + 9,991 > 10,000 \)[/tex] is [tex]\( x > 9 \)[/tex].
