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Evaluate algebraic expressions by substitution

The learner interprets a variable as a quantity represented by a number and evaluates an algebraic expression by replacing variables with given values, including integers, fractions, or decimals, then applying parentheses, operations, and simple whole-number exponents in the correct order. This includes recognizing that substitution requires grouping substituted negative values and that equivalent expressions produce the same result; it does not extend to solving equations or manipulating highly generalized expressions symbolically.

Detailed Explanation: Evaluate algebraic expressions by substitution

To evaluate an algebraic expression by substitution, replace each variable with its given value. Then simplify using the order of operations:

  1. Parentheses
  2. Exponents
  3. Multiplication and division
  4. Addition and subtraction

Always use parentheses when substituting a negative number.

Example: Evaluate

2x2+3(y−1)2x^2+3(y-1)

when x=−2x=-2 and y=12y=\frac12.

Step 1: Substitute the given values

Replace xx with −2-2 and yy with 12\frac12:

2(−2)2+3(12−1)2(-2)^2+3\left(\frac12-1\right)

The parentheses around −2-2 are important because the negative number is being squared.

Step 2: Simplify the parentheses and exponent

(−2)2=4(-2)^2=4

and

12−1=−12\frac12-1=-\frac12

So the expression becomes

2(4)+3(−12)2(4)+3\left(-\frac12\right)

Step 3: Multiply

8−328-\frac32

Step 4: Subtract

Rewrite 88 as 162\frac{16}{2}:

162−32=132\frac{16}{2}-\frac{3}{2}=\frac{13}{2}

Therefore,

132\boxed{\frac{13}{2}}

The value of the expression is 132\frac{13}{2}, or 6.56.5.

Learn by doing: Evaluate algebraic expressions by substitution

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    Algebraic Function Variable Substitution - Simple Terms (Negatives)

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