Algebraic Expressions • Topic 7 of 7

Evaluating Expressions

To evaluate an expression, substitute the given value for each variable and then compute, following the order of operations (parentheses, exponents, multiplication/division, addition/subtraction). Use parentheses around substituted values, especially negatives, to avoid sign mistakes: if x = −2, then x² = (−2)² = 4, not −4. Evaluating turns an abstract expression into a number and is the basis of checking solutions, building tables of values and reading function outputs. On the SAT, careful substitution and order of operations prevent the small slips that cost easy points.

✅ Solved examples

1. Evaluate 3x + 4 when x = 5.
3(5) + 4 = 15 + 4 = 19.
2. Evaluate x² − 2x when x = 3.
3² − 2(3) = 9 − 6 = 3.
3. Evaluate 2x + y when x = 4 and y = −1.
2(4) + (−1) = 8 − 1 = 7.
4. Evaluate x² when x = −5.
(−5)² = 25.

✏️ Practice — try these, take hints as needed

1. Evaluate 4x − 1 when x = 3.
Substitute x = 3.
4(3) − 1.
Compute.
11.
2. Evaluate x² + x when x = 4.
Substitute x = 4.
16 + 4.
Compute.
20.
3. Evaluate 3x − 2y when x = 2 and y = 3.
Substitute both values.
3(2) − 2(3).
6 − 6.
0.
4. Evaluate 2x² when x = −3.
Square first: (−3)² = 9.
Then × 2.
Compute.
18.
5. Evaluate 5 − x when x = −2.
Substitute x = −2.
5 − (−2).
Subtracting a negative adds.
7.

📝 Topic test — 8 questions

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