The model below represents the equation [tex]x+4=4x+2[/tex]. What value of [tex]x[/tex] makes the equation true?
A. [tex]\frac{2}{3}[/tex]
B. 2
C. [tex]\frac{6}{5}[/tex]
D. 4
Answer (2)
Subtract x from both sides: 4 = 3 x + 2 .
Subtract 2 from both sides: 2 = 3 x .
Divide both sides by 3: x = 3 2 .
The solution is x = 3 2 .
Explanation
Understanding the Problem We are given the equation x + 4 = 4 x + 2 and we need to find the value of x that makes this equation true. This is a linear equation, and we can solve it by isolating x on one side of the equation.
Subtracting x from both sides First, let's subtract x from both sides of the equation: x + 4 − x = 4 x + 2 − x 4 = 3 x + 2
Subtracting 2 from both sides Next, we subtract 2 from both sides of the equation: 4 − 2 = 3 x + 2 − 2 2 = 3 x
Dividing by 3 Now, we divide both sides of the equation by 3 to solve for x :
3 2 = 3 3 x x = 3 2
Verification To verify our solution, we substitute x = 3 2 back into the original equation: 3 2 + 4 = 4 ( 3 2 ) + 2 3 2 + 3 12 = 3 8 + 3 6 3 14 = 3 14 Since both sides of the equation are equal, our solution is correct.
Final Answer Therefore, the value of x that makes the equation true is 3 2 .
Examples
Imagine you're trying to balance a seesaw. On one side, you have a weight 'x' plus an additional 4 pounds. On the other side, you have 4 times the weight 'x' plus an additional 2 pounds. Solving the equation x + 4 = 4 x + 2 helps you find the exact weight 'x' needed to perfectly balance the seesaw. This type of problem is useful in many real-world scenarios, such as balancing chemical equations, designing structures, or managing budgets, where maintaining equality is crucial.
The value of x that makes the equation x + 4 = 4 x + 2 true is 3 2 .
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