Solution To Equation Verification

To verify whether a specific number is the solution to an algebraic equation, substitute the given number into the equation in place of the variable $x$ .
Evaluate and simplify the arithmetic operations on the side of the equation containing the variable.
If the simplified left-hand side equals the right-hand side, the statement is true, confirming that the substituted number is indeed the valid solution to the equation.

Objective: Show that $-5$ is the solution to the equation $x - 6 = -11$ .
Step 1: Write the initial equation: $x - 6 = -11$
Step 2: Substitute $-5$ for the variable $x$ : $-5 - 6 = -11$
Step 3: Evaluate the left side of the equality statement: $-5 - 6 = -11$
Conclusion: $-5 - 6$ equals $-11$ , which results in a true statement. Therefore, $-5$ is verified as the solution to the equation.

Objective: Show that $-3$ is the solution to the equation $5x + 14 = -1$ .
Step 1: Write the initial equation: $5x + 14 = -1$
Step 2: Substitute $-3$ for the variable $x$ : $5(-3) + 14 = -1$
Step 3: Perform multiplication to simplify the expression on the left-hand side: $5 \times (-3) = -15$
Step 4: Substitute $-15$ back into the left-hand expression: $-15 + 14 = -1$
Step 5: Evaluate the addition on the left-hand side: $-15 + 14 = -1$
Conclusion: $-15 + 14$ equals $-1$ , which forms a true statement. Therefore, $-3$ is verified as the solution to the equation.