Evaluating expressions drills

Substitute values into algebraic expressions and evaluate.

Free, timed SHSAT practice sets on evaluating expressions— every question includes a full worked explanation, and there's no account required.

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How to evaluate algebraic expressions

Replace each letter with its value in parentheses, then follow the order of operations: parentheses, exponents, multiply and divide, add and subtract.

Example: evaluate \(2a + 3b\) when \(a = -4\) and \(b = 5\). Write \(2(-4) + 3(5) = -8 + 15 = 7\). The parentheses keep the negative sign attached to the number.

Common traps:

Worked examples

Example 1.
Evaluate \(-9x + 8y - 7\) when \(x = 5\) and \(y = -4\).
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Answer:
A

Substitute: \(-9(5) + 8(-4) - 7 = -45 - 32 - 7 = -84\). (Putting \(-4\) in for \(x\) and \(5\) in for \(y\) gives \(69\). Using \(4\) instead of \(-4\) for \(y\) gives \(-20\). Leaving off the \(- 7\) at the end gives \(-77\).)

Example 2.
Evaluate \(\dfrac{-18x - 60}{6}\) when \(x = -2\).
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Answer:
B

Evaluate the numerator first: \(-18(-2) - 60 = -24\), then divide by \(6\): \(-24 \div 6 = -4\). (Dividing only the \(-18x\) term by \(6\) gives \(-54\). Stopping before the division gives \(-24\). Using \(2\) instead of \(-2\) for \(x\) gives \(-16\).)

Example 3.
Evaluate \(8x + 4^2 - 3\) when \(x = -1\).
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Answer:
C

Compute the exponent first, \(4^2 = 16\), then \(8(-1) = -8\), so the total is \(-8 + 16 - 3 = 5\). (Reading \(4^2\) as \(4 \times 2\) gives \(-3\). Using \(1\) instead of \(-1\) for \(x\) gives \(21\). Leaving off the \(- 3\) at the end gives \(8\).)