Question

Solve the equation. Check your solution.

2/5n + 1/10 = 1/2 (n+4)

Answer 1

Solve the equation by eliminating the fractions and simplifying the expression. After combining like terms and isolating the variable, the solution is n=19. This solution can be checked by substituting back into the original equation.

Step-by-step explanation:

To solve the equation 2/5n + 1/10 = 1/2 (n+4), we first need to get rid of the fractions by finding a common denominator, which in this case is 10. Multiply each term by 10 to eliminate the fractions.

Step 1: Multiply each term by 10:

• 10*(2/5n) + 10*(1/10) = 10*(1/2)*(n+4)

Step 2: Simplify the equation:

• 4n + 1 = 5(n+4)

Step 3: Distribute and combine like terms:

• 4n + 1 = 5n + 20

Step 4: Isolate the variable, n:

• 20 - 1 = 5n - 4n
• 19 = n

Step 5: Check your solution by plugging n=19 back into the original equation:

• 2/5(19) + 1/10 should equal 1/2(19 + 4)

The solution n=19 is correct.