Fiona solved the equation shown:
[tex]$\frac{1}{2}-\frac{1}{3}(5 x-3)=\frac{13}{2}$[/tex]
Answer (1)
Multiply both sides by 6 to eliminate fractions: 3 − 2 ( 5 x − 3 ) = 39 .
Expand and simplify: 9 − 10 x = 39 .
Subtract 9 from both sides: − 10 x = 30 .
Divide by -10 to find the solution: x = − 3 .
Explanation
Understanding the Problem We are given the equation 2 1 − 3 1 ( 5 x − 3 ) = 2 13 and we want to solve for x .
Eliminating Fractions First, we multiply both sides of the equation by 6 to eliminate the fractions. This gives us: 6 × ( 2 1 − 3 1 ( 5 x − 3 ) ) = 6 × 2 13 Simplifying, we get: 3 − 2 ( 5 x − 3 ) = 39
Expanding the Equation Next, we expand the left side of the equation: 3 − 10 x + 6 = 39
Combining Like Terms Combining like terms on the left side, we have: 9 − 10 x = 39
Isolating the x Term Now, we subtract 9 from both sides of the equation: − 10 x = 30
Solving for x Finally, we divide both sides by -10 to solve for x :
x = − 10 30 = − 3
Final Answer Thus, the solution to the equation is x = − 3 .
Examples
Imagine you're baking a cake and need to adjust a recipe that uses fractions. Solving equations like this helps you determine the exact amount of each ingredient needed to get the perfect result. Understanding how to manipulate and solve such equations is crucial in various real-life scenarios, from cooking to managing finances or planning projects.
