You're absolutely correct! The solution to the inequality `2x + 4 ≥ 24` is `x ≥ 10`.
Here's a step-by-step explanation of how to solve it and why the number line graph is correct:
---
Step 1: Isolate the variable term
The goal is to get `x` by itself on one side of the inequality.
We start with:
`2x + 4 ≥ 24`
To eliminate the `+4`, we subtract `4` from
both sides. This keeps the inequality balanced.
```
2x + 4 - 4 ≥ 24 - 4
```
Simplifying:
`2x ≥ 20`
---
Step 2: Solve for x
Now, we need to get rid of the coefficient `2` that’s multiplying `x`. We do this by dividing
both sides by `2`.
```
(2x)/2 ≥ 20/2
```
Simplifying:
`x ≥ 10`
---
Step 3: Graph the solution on a number line
The solution `x ≥ 10` means that `x` can be
10 or any number greater than 10.
On the number line:
- We place a
closed circle (●) at `10` because `10` is included in the solution (the inequality is "greater than
or equal to").
- We draw an
arrow pointing to the right from `10` to show that all numbers greater than `10` are also part of the solution.
This matches the red graph shown in your image — a closed dot at 10 and a ray extending to the right.
---
✔ Final Answer: `x ≥ 10`
Your work is perfect — you correctly solved the inequality and represented it on the number line!
Parent Tip: Review the logic above to help your child master the concept of solving inequalities worksheet kuta.
