Let's solve the inequality step-by-step.
1. Understanding the inequality:
We start with the given inequality:
[tex]\[
2764 + x \geq 5000
\][/tex]
Our goal is to find the value of [tex]\( x \)[/tex] that makes this inequality true.
2. Isolate [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the inequality. We do this by subtracting 2764 from both sides of the inequality:
[tex]\[
2764 + x - 2764 \geq 5000 - 2764
\][/tex]
Simplifying this, we have:
[tex]\[
x \geq 5000 - 2764
\][/tex]
3. Calculate the right-hand side:
Next, we perform the subtraction on the right-hand side:
[tex]\[
5000 - 2764 = 2236
\][/tex]
4. Solution to the inequality:
Therefore, the inequality simplifies to:
[tex]\[
x \geq 2236
\][/tex]
This means that the family needs to save at least [tex]\( \$ 2236 \)[/tex] more to reach their goal of [tex]\( \$ 5000 \)[/tex].
Given the options:
- [tex]\( x \geq 2236 \)[/tex]
- [tex]\( x \geq 7764 \)[/tex]
- [tex]\( x \leq 2236 \)[/tex]
- [tex]\( x \leq 7764 \)[/tex]
The correct solution is:
[tex]\[
x \geq 2236
\][/tex]
