Assignment: Solving an Inequality

Li's family is saving money for their summer vacation. Their vacation savings account currently has a balance of [tex]$\$[/tex] 2,764[tex]$. The family would like to have at least $[/tex]\[tex]$ 5,000$[/tex].

The inequality [tex]$2764 + x \geq 5000$[/tex] can be used to determine the amount of money the family still needs to save. What is the solution to the inequality?

A. [tex]$x \geq 2236$[/tex]
B. [tex]$x \geq 7764$[/tex]
C. [tex]$x \leq 2236$[/tex]
D. [tex]$x \leq 7764$[/tex]



Answer :

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]