3(x – 4) = 2(–2x + 1)
The Correct Answer and Explanation is :
To solve the equation ( 3(x – 4) = 2(-2x + 1) ), let’s break it down step by step:
Step 1: Distribute the constants on both sides
Distribute the 3 on the left-hand side and the 2 on the right-hand side:
[
3(x – 4) = 2(-2x + 1)
]
Distribute:
[
3 \cdot x – 3 \cdot 4 = 2 \cdot (-2x) + 2 \cdot 1
]
Simplifying both sides:
[
3x – 12 = -4x + 2
]
Step 2: Move all terms with ( x ) to one side
To get all the terms with ( x ) on one side, add ( 4x ) to both sides:
[
3x + 4x – 12 = 2
]
Simplifying:
[
7x – 12 = 2
]
Step 3: Move the constant term to the other side
Now, add 12 to both sides to isolate the term with ( x ):
[
7x – 12 + 12 = 2 + 12
]
Simplifying:
[
7x = 14
]
Step 4: Solve for ( x )
Now divide both sides of the equation by 7 to solve for ( x ):
[
x = \frac{14}{7}
]
Simplifying:
[
x = 2
]
Final Answer:
The solution to the equation is ( x = 2 ).
Explanation:
The process we used is the method of solving linear equations. We started by applying the distributive property to eliminate parentheses. Next, we collected all terms involving ( x ) on one side of the equation and constants on the other side. Finally, we solved for ( x ) by performing simple arithmetic (addition and division). This method is widely used to solve linear equations, ensuring that the value of ( x ) satisfies both sides of the original equation.