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Solve Equations by Substitution
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Determine whether the given value for the variable is the solution to the equation.
2n+5=27; n=11
Substitute the value for the variable.
2⋅11+5=?27
The value for n is 11, so replace n with 11.
Think About ItWhy does the equals sign have a question mark above it?
While the expression on the left has a variable, the expression has no value. Once we replace the variable with a number, the expression immediately has a value. Until we simplify that expression, we don’t know what this value is and whether or not it’s the same value as the expression on the right. Therefore, we place a question mark over the equals sign to show that we don’t know whether the expressions are equal.
Simplify.
2⋅11+5=?27
22+5=?27
27=27
The left side of the equation has an expression that must be simplified. Follow the order of operations. First, multiply 2 by 11 to get 22. Then, add 22 and 5 to get 27. Since the expression on the left is the same as the expression on the right, the expressions are equal.
Conclude.
n=11 is the solution to the equation.
Since substituting 11 for n resulted in the expression on the left equaling the expression on the right, 11 is the solution to the equation.
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