Solve the equation. [tex]$\frac{2 x+5}{3-x}=\frac{14}{15}$[/tex]
Answer (2)
Multiply both sides by 15 ( 3 − x ) to get 15 ( 2 x + 5 ) = 14 ( 3 − x ) .
Expand both sides: 30 x + 75 = 42 − 14 x .
Simplify to isolate x : 44 x = − 33 .
Solve for x and simplify: x = − 4 3 .
Explanation
Understanding the Problem We are given the equation 3 − x 2 x + 5 = 15 14 . Our goal is to solve for x .
Eliminating Fractions To eliminate the fractions, we multiply both sides of the equation by 15 ( 3 − x ) . This gives us: 15 ( 2 x + 5 ) = 14 ( 3 − x ) .
Expanding the Equation Next, we expand both sides of the equation: 30 x + 75 = 42 − 14 x .
Combining Like Terms Now, we add 14 x to both sides of the equation: 30 x + 14 x + 75 = 42 − 14 x + 14 x which simplifies to 44 x + 75 = 42 .
Isolating the Variable Term Subtract 75 from both sides: 44 x + 75 − 75 = 42 − 75 which simplifies to 44 x = − 33 .
Solving for x Divide both sides by 44: 44 44 x = 44 − 33 which simplifies to x = − 44 33 .
Simplifying the Solution Finally, we simplify the fraction: x = − 4 × 11 3 × 11 = − 4 3 . Therefore, the solution to the equation is x = − 4 3 .
Examples
When designing a bridge, engineers use equations to calculate the forces and stresses acting on different parts of the structure. Solving equations like this helps them determine the correct dimensions and materials needed to ensure the bridge is stable and safe. Similarly, in electrical engineering, such equations are used to analyze circuits and determine the values of components needed for the circuit to function correctly.
The solution to the equation 3 − x 2 x + 5 = 15 14 is x = − 4 3 . This was achieved by eliminating fractions, expanding, and isolating the variable term. Simplifying the final result gave the answer.
;
