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 (2)
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 find the solution: x = 3 4 .
Explanation
Problem Analysis We are given the equation − x + 7 3 = 2 x − 7 25 and we need to find the value of x that satisfies this equation.
Adding x to both sides First, let's add x to both sides of the equation to group the x terms on one side: 7 3 = 2 x + x − 7 25 7 3 = 3 x − 7 25
Adding 25/7 to both sides Next, add 7 25 to both sides to isolate the x term: 7 3 + 7 25 = 3 x 7 28 = 3 x
Simplifying the fraction Simplify the fraction on the left side: 4 = 3 x
Dividing by 3 Finally, divide both sides by 3 to solve for 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 you're 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 type of problem is useful in various real-life scenarios, such as balancing chemical equations, calculating electrical circuits, or even managing financial budgets where you need to find the equilibrium point.
The solution for the equation − x + 7 3 = 2 x − 7 25 is found to be x = 3 4 . Thus, the correct answer is option B.
;
