You're given the equation:
>
2 |2x - 4| = 18
And you’re shown two checks — for
x = -5/2 and
x = 13/2 — both of which satisfy the equation, leading to the solution set:
>
{-5/2, 13/2}
Let’s solve this step-by-step and explain why these are the correct solutions.
---
## 🔍 Step 1: Understand the equation
We have an absolute value equation:
>
2 |2x - 4| = 18
Absolute value equations often have
two solutions, because |A| = B (with B ≥ 0) implies A = B or A = -B.
---
## 🧮 Step 2: Isolate the absolute value
Divide both sides by 2 to isolate the absolute value:
>
|2x - 4| = 9
---
## 📐 Step 3: Break into two cases
The definition of absolute value says:
> If |A| = B, then A = B
or A = -B (provided B ≥ 0 — which it is here, since 9 > 0)
So we write two equations:
Case 1:
>
2x - 4 = 9
Solve for x:
> 2x = 9 + 4
> 2x = 13
>
x = 13/2
Case 2:
>
2x - 4 = -9
Solve for x:
> 2x = -9 + 4
> 2x = -5
>
x = -5/2
---
##
✔ Step 4: Check both solutions (as shown in your image)
Check x = -5/2:
Plug into original equation:
> 2 |2(-5/2) - 4| = 2 |-5 - 4| = 2 |-9| = 2 * 9 =
18 ✔️
Check x = 13/2:
> 2 |2(13/2) - 4| = 2 |13 - 4| = 2 |9| = 2 * 9 =
18 ✔️
Both work!
---
## 🎯 Final Answer:
>
Solution set: {-5/2, 13/2}
This matches what was shown in your image — and now you understand
why those are the only two solutions.
---
## 💡 Key Takeaway:
When solving equations with absolute values:
1. Isolate the absolute value expression.
2. Split into two separate equations: one where the inside equals the positive value, and one where it equals the negative.
3. Solve both.
4. Always check your solutions in the original equation — especially if you multiplied/divided or squared during solving (though not needed here).
✔ You’ve got it!
Parent Tip: Review the logic above to help your child master the concept of absolute value questions.
