Select all the equation that have the same solution as the equation 3x-12=24
A: 15 x -60=120
b: 3x=12
c: 3 x =36
d: x-4=8
e: 12x -12=24
The Correct Answer and Explanation is:
To determine which equations have the same solution as the equation:
Original Equation:
3x – 12 = 24
Step 1: Solve the original equation
We’ll solve for x: 3x−12=243x – 12 = 24
Add 12 to both sides: 3x=363x = 36
Now divide both sides by 3: x=12x = 12
So the solution to the original equation is: x=12x = 12
Step 2: Check which other equations also have the solution x = 12
Let’s test each option:
A. 15x – 60 = 120
Substitute x = 12: 15(12)−60=180−60=120✓15(12) – 60 = 180 – 60 = 120 ✓
✅ True, so A is correct
B. 3x = 12
Substitute x = 12: 3(12)=36≠12✗3(12) = 36 ≠ 12 ✗
❌ False, so B is incorrect
C. 3x = 36
Substitute x = 12: 3(12)=36✓3(12) = 36 ✓
✅ True, so C is correct
D. x – 4 = 8
Substitute x = 12: 12−4=8✓12 – 4 = 8 ✓
✅ True, so D is correct
E. 12x – 12 = 24
Substitute x = 12: 12(12)−12=144−12=132≠24✗12(12) – 12 = 144 – 12 = 132 ≠ 24 ✗
❌ False, so E is incorrect
✅ Final Answer: A, C, and D
🧠 Explanation (300+ words):
To find all equations that share the same solution as a given equation, we begin by solving the original equation for x. The equation 3x – 12 = 24 is a linear equation, and solving it involves isolating the variable:
First, we add 12 to both sides to eliminate the constant on the left-hand side: 3x−12+12=24+12⇒3x=363x – 12 + 12 = 24 + 12 \Rightarrow 3x = 36
Then divide both sides by 3: x=12x = 12
This means that any other equation that is also true when x = 12 has the same solution.
For example, in option A, the equation is 15x – 60 = 120. Plugging in x = 12 gives us: 15(12)−60=180−60=12015(12) – 60 = 180 – 60 = 120
Which is true, so A has the same solution.
Option C is already simplified to 3x = 36, which matches the transformed version of our original equation—clearly, it has the same solution.
Option D says x – 4 = 8, which simplifies to x = 12 when solved. So it also matches.
On the other hand, option B results in 3x = 12, and solving this gives x = 4—not a match.
Option E results in 12x – 12 = 24. Solving this: 12x=36⇒x=312x = 36 \Rightarrow x = 3
Again, not equal to 12.