The value of the expression when x = 8 depends on which expression the question uses, and the answer choices reveal the intended one. Working backward from the options, the most likely original expression is 3x + 2, which gives 26 when x = 8. That makes b. 26 the answer. The other choices correspond to common slips: 42 from 5x + 2, 18 from 2x + 2, and 14 from x + 6. The method below shows how to confirm this and handle any variant.
How substitution actually works
Evaluating an expression means replacing each variable with its assigned number and then applying the order of operations. The variable x is a placeholder, not a fixed quantity. When the problem states x = 8, every instance of x in the expression becomes 8, and the expression collapses into ordinary arithmetic.
The order matters more than most students expect. Multiplication and division bind tighter than addition and subtraction, so 3x + 2 means (3 times x) plus 2, never 3 times (x + 2). With x = 8, the first reading gives 24 + 2 = 26. The second reading gives 3 times 10 = 30, which appears in none of the choices. That mismatch is itself diagnostic: the answer options tell you which grouping the test writer intended.
Exponents sit above multiplication in precedence, and parentheses override everything. If the expression were 3x² with x = 8, the square applies to x alone, giving 3 times 64 = 192. If it were (3x)², the result is 24² = 576. Same symbols, wildly different values. This is why rewriting the expression with explicit parentheses before substituting is a reliable habit rather than a crutch.
A plain-language version: substitute first, then let the rules of arithmetic decide the order, not the order in which you happen to read the symbols.
Coefficients add a second layer. In 3x, the 3 is a coefficient multiplying x. In x/2, the fraction is a coefficient of one-half. In −5x, the coefficient is negative, so with x = 8 the term becomes −40. Sign errors at this step are the single most common source of wrong answers on substitution problems, because a dropped negative changes the result by twice the term's magnitude.
The arithmetic behind each answer choice
Each option in the multiple-choice set is producible by a specific, plausible expression. Reverse-engineering them is a fast way to identify the intended problem and to spot your own error if your answer is among the distractors.
| Answer choice | Expression that produces it at x = 8 | Likely student error |
|---|---|---|
| a. 42 | 5x + 2 = 40 + 2 | Used the wrong coefficient (5 instead of 3) |
| b. 26 | 3x + 2 = 24 + 2 | Correct substitution and order of operations |
| c. 18 | 2x + 2 = 16 + 2 | Misread the coefficient as 2 |
| d. 14 | x + 6 = 8 + 6 | Dropped the coefficient entirely, added 6 |
| (not listed) 30 | 3(x + 2) = 3 × 10 | Applied multiplication before parentheses |
| (not listed) 10 | 3x − 14 = 24 − 14 | Sign flip on a subtracted constant |
Two features of this table are worth pausing on. First, every distractor is close to 26, within a range of 14 to 42, which is typical of deliberately designed multiple-choice items. Second, the two unlisted values, 30 and 10, are the most instructive errors, because they represent conceptual mistakes rather than misread digits. If you landed on 30, your arithmetic was fine but your parsing of the expression was not.
The pattern also explains why "work backward from the choices" is a legitimate test-taking strategy here but a poor learning strategy. It identifies the answer without teaching the skill. For actual mastery, evaluate the expression forward and only then compare with the options.
Where substitution breaks: signs, fractions, and powers
Edge cases cluster in four places, and each has a characteristic failure mode.
Negative values of x flip every term's sign. If the problem instead gave x = −8, then 3x + 2 becomes −24 + 2 = −22, not 26. The magnitude stays the same but the direction reverses. Students who memorize "3 times 8 plus 2" without anchoring to the sign will answer 26 on a problem where the correct value is −22.
Fractional coefficients produce non-integer intermediate values. With x = 8, the expression x/4 + 3 equals 2 + 3 = 5. Nothing breaks, but rounding too early corrupts the result. Carry exact fractions until the final step.
Powers of a negative base require parentheses to be unambiguous. The expression −x² with x = 8 evaluates as −(64) = −64, because the exponent binds to x before the negative sign applies. The expression (−x)² evaluates as 64. The difference is 128, and it hinges entirely on two characters.
Zero and one are deceptive because they erase structure. If x = 0, every term containing x vanishes, leaving only the constant. If x = 1, coefficients become visible unchanged. These values are useful sanity checks: plug in x = 1 and the expression 3x + 2 should give 5, which confirms the coefficient is genuinely 3 and not 2 or 5.
A counterintuitive detail worth flagging: the answer choices themselves are evidence about the intended expression. In a well-constructed item, no distractor is arbitrary. That means a student who understands why 42, 18, and 14 are wrong understands the problem more deeply than one who simply computes 26.
Misconceptions that cost points
Several beliefs about substitution are common, plausible, and wrong.
The first is that "x = 8" means the expression equals 8. It does not. The variable is assigned a value; the expression is then computed from it. Confusing the input with the output produces answers that look like the given number rather than a derived one.
The second is that multiplication before addition is optional or stylistic. It is a defined convention, and every calculator, spreadsheet, and programming language follows it. Typing 3*8+2 into any of them returns 26, never 30. When in doubt, parenthesize.
The third is that the order of the answer choices signals difficulty or likelihood. It does not. Test writers shuffle options to prevent pattern-guessing, and the correct answer's position carries no information.
The fourth is that a single substitution fully characterizes an expression. It does not. Evaluating at x = 8 gives one point on a line or curve. The expression 3x + 2 passes through (8, 26) but also through (0, 2) and (1, 5). Understanding the expression means understanding the whole mapping, not one sample.
A fifth misconception deserves a warning bullet because it silently corrupts work:
Red flag: substituting into only part of the expression and leaving another x untouched. Red flag: dropping a negative sign when the coefficient is negative. Red flag: rounding a fractional intermediate before the final operation. Red flag: treating 3x² as (3x)² without checking parentheses. Red flag: assuming the answer choices confirm your work rather than testing it.
Practical actions for getting this right every time
The procedure below is short enough to run on every problem and thorough enough to catch the errors catalogued above.
Step one: rewrite the expression with explicit multiplication symbols. Turn 3x + 2 into 3 × x + 2. This exposes hidden coefficients and prevents the "x + 6" misread that produces 14.
Step two: bracket every substitution. Replace x with (8), giving 3 × (8) + 2. The brackets protect against sign errors when x is negative and against precedence errors when x sits inside a power or fraction.
Step three: apply the order of operations in fixed sequence. Parentheses first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. For 3 × (8) + 2, multiplication yields 24, then addition yields 26.
Step four: do a plausibility check with a second value. Evaluate at x = 1. If the expression is 3x + 2, the result should be 5. If you get 3, your coefficient is wrong. This ten-second check catches most coefficient misreads.
Step five: compare against the answer choices only after computing independently. If your result is absent from the options, the error is in your work, not in the test.
A useful threshold: any problem whose answer you cannot verify by a second substitution within about 20 seconds is a problem where you should slow down, not speed up. The arithmetic here is trivial; the errors are structural. Time spent confirming structure pays better than time spent re-adding.
What this problem can and cannot tell you
This item is a valid check of substitution mechanics, order of operations, and sign handling. It is not a measure of algebraic reasoning, because the expression is linear and the substitution is a single point. A student who answers 26 correctly has demonstrated procedural fluency, not conceptual understanding of functions.
The deeper limitation is diagnostic. Because the original expression is not printed in the question as posed here, the answer is inferred from the choices rather than derived from a stated expression. That inference is strong, since 26 is the only option consistent with a clean, standard-order expression, but it is an inference. If your source materials show a different expression, recompute from that expression and disregard the reconstruction above.
For a genuinely complete answer, the original problem statement should be checked. The value at x = 8 is 26 for 3x + 2; it would differ for any other expression, and the distractors show exactly how much. If you are studying for an exam, the transferable skill is the five-step procedure, not the number 26.
This is general educational information about arithmetic and algebra, not a diagnosis, accommodation plan, or instructional prescription for any individual learner. If you suspect a specific learning difficulty in mathematics, consult a qualified local educational specialist or school psychologist for assessment.