Select the correct answer.
What is the solution for $x$ in the equation?
$\frac{5}{3} x+4=\frac{2}{3} x$
A. $x=-\frac{1}{7}$
B. $x=4$
C. $x=-4$
D. $x=\frac{12}{7}$
Answer (1)
Subtract 3 2 x from both sides: 3 5 x − 3 2 x + 4 = 0 .
Simplify the equation: x + 4 = 0 .
Subtract 4 from both sides to solve for x : x = − 4 .
The solution is x = − 4 .
Explanation
Problem Analysis We are given the equation 3 5 x + 4 = 3 2 x and we want to solve for x .
Isolating x terms First, we subtract 3 2 x from both sides of the equation to get all the x terms on one side: 3 5 x − 3 2 x + 4 = 3 2 x − 3 2 x
Simplifying Simplifying both sides, we have: 3 3 x + 4 = 0
Further simplification Since 3 3 = 1 , we can further simplify to: x + 4 = 0
Isolating x Now, we subtract 4 from both sides of the equation to isolate x :
x + 4 − 4 = 0 − 4
Solution This gives us the solution: x = − 4
Examples
Imagine you're balancing a seesaw. On one side, you have 3 5 of a friend plus 4 bricks, and on the other side, you have 3 2 of the same friend. To find out how much 'weight' each friend represents, you need to solve the equation. This type of problem helps in understanding how to balance equations, which is useful in many real-life situations like managing budgets or calculating mixtures.
