Step 1 :Given the equation \(2 \cdot(x+5)-3 \cdot(5-x)=10\)
Step 2 :First, distribute the 2 and -3 into the parentheses to get \(2x + 10 - 15 + 3x = 10\)
Step 3 :Simplify the equation to get \(5x - 5 = 10\)
Step 4 :Add 5 to both sides of the equation to get \(5x = 15\)
Step 5 :Finally, divide both sides by 5 to solve for x, which gives us \(x = 3\)
Step 6 :\(\boxed{x = 3}\) is the solution to the equation \(2 \cdot(x+5)-3 \cdot(5-x)=10\) in the universe of rational numbers