Final answer:
An equivalent equation to the given equation 1/2(6x+8)=x+4/10 is 3x+4=x+4/5. This is achieved by performing the same operations on both sides of the equation, including multiplication and simplification.
Step-by-step explanation:
The question asks for an equation that is equivalent to the given expression 1/2(6x+8)=x+4/10. To find the equivalent equation, we need to perform the same operation on both sides of the equals sign. If we multiply both sides of the given equation by 2, we get 6x + 8 = 2x + 0.8. Now, to have an equation with the same value on both sides but in a different form, we subtract 2x from both sides to get 4x + 8 = 0.8. To convert 0.8 to a fraction that has the same value, we can write it as 4/5, because 0.8 is equivalent to 4/5. Hence, the equivalent equation is 4x + 8 = 4/5, which after simplifying becomes 20x + 40 = 4, and then 5x + 10 = 1, and finally, 3x + 4 = x + 4/5.