Questions: Solve the equation. Check you 18=8-(n+10)

Transcript text: Solve the equation. Check you \[ 18=8-(n+10) \]

Solution

Solution Steps

To solve the equation \( 18 = 8 - (n + 10) \), we need to isolate the variable \( n \). First, simplify the right-hand side of the equation, then solve for \( n \) by performing the necessary arithmetic operations.

Step 1: Simplify the Right-Hand Side

Given the equation: \[ 18 = 8 - (n + 10) \] First, simplify the right-hand side: \[ 18 = 8 - n - 10 \]

Step 2: Combine Like Terms

Combine the constants on the right-hand side: \[ 18 = -n - 2 \]

Step 3: Isolate \( n \)

To isolate \( n \), add 2 to both sides of the equation: \[ 18 + 2 = -n \] \[ 20 = -n \] Multiply both sides by -1 to solve for \( n \): \[ n = -20 \]

Step 4: Verify the Solution

Substitute \( n = -20 \) back into the original equation to verify: \[ 18 = 8 - (-20 + 10) \] Simplify inside the parentheses: \[ 18 = 8 - (-10) \] \[ 18 = 8 + 10 \] \[ 18 = 18 \] Both sides of the equation are equal, confirming that the solution is correct.

Final Answer

\(\boxed{n = -20}\)

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