Select the correct answer.
What is the solution for $x$ in the equation?
$-x+\frac{3}{7}=2 x-\frac{25}{7}$
A. $x=\frac{4}{3}$
B. $x=-\frac{4}{3}$
C. $x=\frac{3}{4}$
D. $x=-\frac{3}{4}$
Answer (1)
Add x to both sides: 7 3 = 3 x − 7 25 .
Add 7 25 to both sides: 7 28 = 3 x .
Simplify: 4 = 3 x .
Divide by 3: x = 3 4 .
Explanation
Problem Analysis We are given the equation − x + 7 3 = 2 x − 7 25 and asked to solve for x . Our goal is to isolate x on one side of the equation.
Adding x to both sides First, let's add x to both sides of the equation to get the x terms on the right side: 7 3 = 2 x + x − 7 25 7 3 = 3 x − 7 25
Adding 25/7 to both sides Next, we add 7 25 to both sides of the equation to isolate the x term: 7 3 + 7 25 = 3 x 7 28 = 3 x
Simplifying Now, simplify the left side of the equation: 4 = 3 x
Dividing by 3 Finally, divide both sides by 3 to solve for x : 3 4 = x So, x = 3 4
Examples
Imagine you're balancing a seesaw. On one side, you have a weight represented by 'x' and an additional 3/7 of a unit of weight. On the other side, you have twice the weight 'x' and are missing 25/7 of a unit of weight. Solving this equation helps you find the exact weight 'x' needed to perfectly balance the seesaw. This principle extends to many real-world scenarios, such as balancing chemical equations, managing financial budgets, or optimizing resource allocation.
