Make a two column proof to solve ½ (4x – 6) = 15.
Sure! Here's a step-by-step solution to solve the equation ½ (4x - 6) = 15:
Step 1: Start with the given equation: ½ (4x - 6) = 15.
Step 2: Distribute the ½ to the terms inside the parentheses: 2x - 3 = 15.
Step 3: Add 3 to both sides of the equation to isolate the variable term: 2x = 18.
Step 4: Divide both sides of the equation by 2 to solve for x: x = 9.
Step 5: Therefore, the solution to the equation ½ (4x - 6) = 15 is x = 9.
| Statements | Reasons |
|----------------------|----------------------------------------------|
| 1. Given | |
| 2. Start with given equation | |
| 3. Distributive property | |
| 4. Simplify the equation | |
| 5. Multiply both sides by 2 | |
| 6. Solve for x | |
| 7. Final answer | |
Statement 1: Given
Statement 2: Start with given equation 1/2(4x - 6) = 15
Statement 3: Distributive property: 1/2(4x) - 1/2(6) = 15
Statement 4: Simplify the equation: 2x - 3 = 15
Statement 5: Multiply both sides by 2: (2x - 3) * 2 = 15 * 2
Statement 6: Solve for x: 4x - 6 = 30
Statement 7: Final answer: x = 9
To solve the equation 1/2(4x - 6) = 15 by using a two-column proof, we need to follow a logical sequence of steps to derive the solution. Here's how we can approach it:
Statement | Reason
---------|-------
1. (1/2)(4x - 6) = 15 | Given
2. 4x - 6 = 30 | Multiply both sides by 2
3. 4x = 36 | Add 6 to both sides
4. x = 9 | Divide both sides by 4
Let's explain each step in detail:
Statement 1: (1/2)(4x - 6) = 15 (Given)
In the given equation, we have the expression (1/2)(4x - 6) on the left side, which is equal to 15 on the right side.
Statement 2: 4x - 6 = 30 (Multiply both sides by 2)
We can multiply both sides of the equation by 2 to eliminate the fraction. This will result in the equation 4x - 6 = 30.
Statement 3: 4x = 36 (Add 6 to both sides)
To isolate the term '4x,' we add 6 to both sides of the equation. This will simplify the equation to 4x = 36.
Statement 4: x = 9 (Divide both sides by 4)
Finally, we divide both sides by 4 to get the value of 'x' alone. This step will give us the solution: x = 9.
By following this two-column proof, we have successfully solved the equation 1/2(4x - 6) = 15 and determined that the value of 'x' is 9.