Question

3/5(х + 7) - 1/2(х - 3) = 6 4/5

Answer 1

$\displaystyle \tt \frac{3}{5}(x+7)-\frac{1}{2}(x-3)=6\frac{4}{5}\\\frac{3}{5}x+\frac{21}{5}-\frac{1}{2}x+\frac{3}{2}=\frac{34}{5}\\\frac{3}{5}x+\frac{57}{10}-\frac{1}{2}x=\frac{34}{5}\\6x+57-5x=68\\x+57=68\\x=68-57\\x=11$

Answer 2

To solve the equation 3/5(x + 7) - 1/2(x - 3) = 6 4/5, we can follow these steps:

1. Simplify both sides of the equation: 3/5(x + 7) - 1/2(x - 3) = 6 4/5

   Distribute the terms inside the parentheses: (3/5)x + (3/5)(7) - (1/2)x + (1/2)(-3) = 6 4/5

   Simplify the fractions: (3/5)x + 21/5 - (1/2)x - 3/2 = 6 4/5

2. Find a common denominator for the fractions. In this case, the common denominator is 10: (6/10)x + 42/10 - (5/10)x - 15/10 = 34/5

3. Combine like terms on both sides of the equation: (6/10)x - (5/10)x + 42/10 - 15/10 = 34/5

   Simplify: (1/10)x + 27/10 = 34/5

4. Convert the mixed number on the right side to an improper fraction: (1/10)x + 27/10 = (34/5)

   To convert 34/5 to a fraction with a denominator of 10, multiply the numerator and denominator by 2: (1/10)x + 27/10 = (68/10)

5. Now, the equation becomes: (1/10)x + 27/10 = 68/10

6. Subtract 27/10 from both sides of the equation to isolate the variable term: (1/10)x + 27/10 - 27/10 = 68/10 - 27/10

   Simplify: (1/10)x = 41/10

7. To solve for x, multiply both sides of the equation by 10/1 to cancel out the denominator on the left side: (10/1)((1/10)x) = (10/1)(41/10)

   Simplify: x = 41/1

8. The solution to the equation is: x = 41