Select the correct answer.
What is the solution for $x$ in the equation?
$-x+\frac{3}{7}=2 x-\frac{25}{7}$
A. $x=\frac{3}{4}$
B. $x=-\frac{3}{4}$
C. $x=\frac{4}{3}$
D. $x=-\frac{4}{3}$
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 to solve for x : x = 3 4 .
Explanation
Problem Analysis We are given the equation − x + 7 3 = 2 x − 7 25 and asked to find the value of x that satisfies it.
Isolating x terms To solve for x , we first want to isolate the terms with x on one side of the equation and the constant terms on the other side. We can start by adding x to both sides of the equation: − x + 7 3 = 2 x − 7 25 − x + 7 3 + x = 2 x − 7 25 + x 7 3 = 3 x − 7 25
Isolating constant terms Next, we add 7 25 to both sides of the equation: 7 3 = 3 x − 7 25 7 3 + 7 25 = 3 x − 7 25 + 7 25 7 28 = 3 x
Simplifying the equation Now, we simplify the fraction 7 28 : 7 28 = 4 So we have: 4 = 3 x
Solving for x Finally, we divide both sides of the equation by 3 to solve for x : 4 = 3 x 3 4 = 3 3 x x = 3 4
Final Answer Therefore, the solution for x is 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. On the other side, you have twice the weight 'x' and are missing 25/7 of a unit to balance it. Solving this equation helps you find the exact weight 'x' needed to make the seesaw perfectly balanced. This concept extends to balancing chemical equations, financial budgets, or any scenario where you need to find an unknown quantity to achieve equilibrium.
