$x+\frac{3}{4}=\frac{6}{7}$
Answer (1)
Subtract 4 3 from both sides: x = 7 6 − 4 3 .
Find the common denominator: x = 28 24 − 28 21 .
Subtract the fractions: x = 28 3 .
The solution is: 28 3 .
Explanation
Understanding the equation We are given the equation x + 4 3 = 7 6 and we need to solve for x . This is a linear equation, and we can isolate x by subtracting 4 3 from both sides of the equation.
Isolating x Subtract 4 3 from both sides of the equation: x = 7 6 − 4 3
Finding a common denominator To subtract the fractions, we need to find a common denominator. The least common multiple of 7 and 4 is 28. So, we rewrite the fractions with the common denominator: x = 7 × 4 6 × 4 − 4 × 7 3 × 7 x = 28 24 − 28 21
Subtracting the fractions Now, we subtract the fractions: x = 28 24 − 21 x = 28 3
Final answer Therefore, the solution is x = 28 3 .
Examples
Imagine you're baking a cake and need to adjust a recipe. If the recipe calls for a certain amount of flour, but you only want to make a fraction of the cake, you need to adjust all the ingredients proportionally. Solving linear equations like this helps you determine the correct amount of each ingredient to use, ensuring your cake turns out perfectly, even when you're scaling the recipe up or down. This is a practical application of algebra in everyday cooking and baking.
