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6.4 Creating and Evaluating Algebraic Expressions

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ACCUPLACER Suite Study Guide Exam

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1 Chapter 1: ACCUPLACER Suite Overview & Testing Mechanics

1.1 The ACCUPLACER Testing System & Computer-Adaptive Mechanics 1.2 Placement Policies, Score Scales & Institutional Cut Scores 1.3 Test-Taking Strategies, Tool Mechanics & Pacing

2 Chapter 2: Next-Generation Reading

2.1 The Reading Test Blueprint: Set-Based and Discrete Items 2.2 Information and Ideas: Close Reading & Central Themes 2.3 Summarizing and Understanding Relationships 2.4 Rhetoric, Text Structure & Author's Purpose 2.5 Analyzing Point of View and Authorial Purpose 2.6 Analyzing Arguments: Claims, Counterclaims, and Evidence 2.7 Synthesis & Paired Text Comparative Analysis 2.8 Vocabulary in Context & Figurative Language 2.9 Passage Genre, Content Area, Mode, and Text Complexity 2.10 Answer-Choice Traps and Evidence Discipline

3 Chapter 3: Next-Generation Writing: Expression of Ideas

3.1 The Writing Test Blueprint: Passage Sets and Content Distribution 3.2 Development: Proposition and Supporting Evidence 3.3 Focus: Adding, Retaining, and Deleting for Relevance 3.4 Organization: Logical Sequence and Paragraph Order 3.5 Introductions, Conclusions, and Transitional Cohesion 3.6 Effective Language Use: Precision and Word Choice 3.7 Concision: Eliminating Wordiness and Redundancy 3.8 Style, Tone, and Voice Consistency 3.9 Syntax: Sentence Combining for Rhetorical Purpose

4 Chapter 4: Next-Generation Writing: Standard English Conventions

4.1 Sentence Boundaries: Fragments, Run-ons, and Comma Splices 4.2 Subordination and Coordination 4.3 Parallel Structure 4.4 Modifier Placement: Misplaced and Dangling Modifiers 4.5 Inappropriate Shifts in Verb Tense 4.6 Inappropriate Shifts in Verb Voice and Mood 4.7 Inappropriate Shifts in Pronoun Person and Number 4.8 Subject-Verb Agreement, Pronoun Case, and Verb Forms 4.9 Possessive Determiners, Contractions, and Confusable Adverbs 4.10 Pronoun Clarity and Pronoun-Antecedent Agreement 4.11 Frequently Confused Words, Noun Agreement, and Logical Comparison 4.12 Within-Sentence Punctuation: Semicolons, Colons, Dashes, and Apostrophes 4.13 Items in a Series and Nonrestrictive Elements 4.14 End-of-Sentence Punctuation, Hyphenation, and Unnecessary Punctuation

5 Chapter 5: Next-Generation Arithmetic

5.1 Whole Number Operations, Estimation & Multi-Step Applications 5.2 Fractions, Mixed Numbers & Operations 5.3 Decimal Operations & Place-Value Conversions 5.4 Percent Calculations, Increase, Decrease, and Applications 5.5 Number Comparisons and Equivalents Across Formats

6 Chapter 6: Next-Generation Quantitative Reasoning, Algebra, and Statistics (QAS)

6.1 Rational Numbers, Absolute Value, and Order of Operations 6.2 Exponents, Radicals, and Scientific Notation 6.3 Ratio, Proportional Relationships, and Unit Conversions 6.4 Creating and Evaluating Algebraic Expressions 6.5 Linear Equations, Inequalities, and Systems of Two Equations 6.6 Linear Applications, Functions, and Graphs 6.7 Probability and Sets 6.8 Descriptive Statistics: Center, Spread, and Graphical Displays 6.9 Geometry for Pre-Algebra and Algebra 1

7 Chapter 7: Next-Generation Advanced Algebra, Quadratics & Polynomials

7.1 Advanced Linear Equations, Systems, and Coordinate Geometry 7.2 Factoring Methods for Quadratics, Cubics, and Polynomials 7.3 Quadratic Equations, Vertex Form & Parabolic Functions 7.4 Polynomial Equations, Roots, and Graphs 7.5 Radical and Rational Equations and Functions 7.6 Geometry for Algebra 1 and Algebra 2

8 Chapter 8: Functions, Exponentials, Logarithms & Trigonometry

8.1 Function Notation, Transformations, Compositions & Inverses 8.2 Domain, Range, and Interpreting Functions in Context 8.3 Exponential & Logarithmic Functions, Laws & Modeling 8.4 Right-Triangle Trigonometry, the Unit Circle, and Radian Measure 8.5 Law of Sines, Law of Cosines, and Trigonometric Equations 8.6 Choosing Your Math Test: Arithmetic, QAS, or AAF

9 Chapter 9: WritePlacer & WritePlacer ESL Essays

9.1 WritePlacer Prompt Format, Planning, and the Writing Process 9.2 The WritePlacer Scoring Rubric & 6 Core Dimensions 9.3 Reading the WritePlacer Score Scale: What Each Band Demonstrates 9.4 Essay Architecture: Thesis, Evidence Integration & Structure 9.5 WritePlacer ESL Scoring Standards & Synthesis

10 Chapter 10: ACCUPLACER ESL Placement Suite

10.1 The ESL Placement Suite: Structure, Scoring, and Score Interpretation 10.2 ESL Reading Skills & Passage Comprehension 10.3 ESL Sentence Meaning & Context Clues 10.4 ESL Language Use & Grammatical Mechanics 10.5 ESL Listening Comprehension & Spoken Contexts

6.4 Creating and Evaluating Algebraic Expressions

Key Takeaways Explain This Topic AI

Algebraic expressions accounts for 2 to 3 of the 20 QAS questions.

An expression has no equals sign and is evaluated; an equation has one and is solved.

Like terms share identical variables raised to identical powers, so 3x squared and 5x cannot be combined.

Translating 'less than' reverses the order of subtraction, making 'five less than x' equal to x minus 5.

Substituting a test value into two expressions is a fast, reliable check for equivalence.

Last updated: August 2026

The Foundation Area

Algebraic expressions: Creating and evaluating expressions to represent situations, and using properties of operations to combine like terms and identify equivalent expressions.

This area carries 2 to 3 of the 20 QAS questions directly, but its real weight is larger — the Linear equations and Linear applications and graphs areas both depend on the translation skills built here.

Expression Versus Equation

An expression has no equals sign: 3 x + 7 3x + 7 3 x + 7 . You evaluate or simplify it.

An equation has one: 3 x + 7 = 22 3x + 7 = 22 3 x + 7 = 22 . You solve it.

Questions asking you to "write an expression" want no equals sign, and an answer choice containing one is wrong on form alone.

Translating Words to Algebra

  • Phrase Operation
  • sum, total, increased by, more than +
  • difference, decreased by, less than, fewer than −
  • product, times, of, twice, triple ×
  • quotient, per, divided by, ratio of ÷
  • is, equals, results in, yields =
  • at most / no more than ≤
  • at least / no less than ≥
  • The Reversal Traps

Two phrases reverse the order of their operands, and both are tested deliberately.

"Less than"

Five less than x → x − 5 x - 5 x − 5 , not 5 − x 5 - x 5 − x .

"Subtracted from"

Five subtracted from x → x − 5 x - 5 x − 5 .

But "x less than five" → 5 − x 5 - x 5 − x . The order in the phrase is the reverse of the order in the expression, so read carefully.

Compare with a phrase that does not reverse:

x decreased by five → x − 5 x - 5 x − 5 (same order)

Division phrasing behaves similarly:

The quotient of x and 4 → x / 4 x/4 x /4 4 divided into x → x / 4 x/4 x /4 x divided by 4 → x / 4 x/4 x /4 4 divided by x → 4 / x 4/x 4/ x

Building Expressions From Context

A technician charges a $65 service fee plus $48 per hour. Write an expression for the total cost of a job lasting h hours.

The fee is fixed; the hourly charge scales with h h h :

65 + 48 h 65 + 48h 65 + 48 h

The structure constant + rate × variable describes a large share of QAS application items. Identifying which quantity is fixed and which scales is the entire modeling step.

A tank holds 400 gallons and drains at 12 gallons per minute. Write an expression for the volume remaining after m minutes.

400 − 12 m 400 - 12m 400 − 12 m

Draining means the rate is subtracted.

Consecutive Integers

  • Description Expressions
  • Consecutive integers n n n , n + 1 n+1 n + 1 , n + 2 n+2 n + 2
  • Consecutive even integers n n n , n + 2 n+2 n + 2 , n + 4 n+4 n + 4
  • Consecutive odd integers n n n , n + 2 n+2 n + 2 , n + 4 n+4 n + 4

Consecutive even and odd integers use the same pattern — the difference is whether n n n starts even or odd. Students often write n + 1 n+1 n + 1 , n + 3 n+3 n + 3 for odd integers, which produces integers of alternating parity.

Evaluating Expressions

Substitute and apply the order of operations. Parentheses around substituted values prevent sign errors.

Evaluate − 2 x 2 + 5 x − 3 -2x^2 + 5x - 3 − 2 x 2 + 5 x − 3 at x = − 3 x = -3 x = − 3 .

− 2 ( − 3 ) 2 + 5 ( − 3 ) − 3 -2(-3)^2 + 5(-3) - 3 − 2 ( − 3 ) 2 + 5 ( − 3 ) − 3 = − 2 ( 9 ) − 15 − 3 = -2(9) - 15 - 3 = − 2 ( 9 ) − 15 − 3 = − 18 − 15 − 3 = − 36 = -18 - 15 - 3 = -36 = − 18 − 15 − 3 = − 36

The critical step is ( − 3 ) 2 = 9 (-3)^2 = 9 ( − 3 ) 2 = 9 , not − 9 -9 − 9 . Exponentiation precedes the coefficient's multiplication, and the parentheses make that visible.

Contrast: − 3 2 = − 9 -3^2 = -9 − 3 2 = − 9 , because without parentheses the exponent binds only to the 3 and the negative sign is applied afterward. Distinguishing ( − 3 ) 2 (-3)^2 ( − 3 ) 2 from − 3 2 -3^2 − 3 2 is one of the highest-frequency arithmetic errors on the test.

Combining Like Terms

Like terms have identical variable parts — same variables, same exponents.

3 x 2 + 5 x − 2 x 2 + 7 x = ( 3 − 2 ) x 2 + ( 5 + 7 ) x = x 2 + 12 x 3x^2 + 5x - 2x^2 + 7x = (3-2)x^2 + (5+7)x = x^2 + 12x 3 x 2 + 5 x − 2 x 2 + 7 x = ( 3 − 2 ) x 2 + ( 5 + 7 ) x = x 2 + 12 x

x 2 x^2 x 2 and x x x are not like terms and never combine. Neither are x y xy x y and x 2 x^2 x 2 .

  • The Distributive Property
  • 3 ( 2 x − 5 ) = 6 x − 15 3(2x - 5) = 6x - 15 3 ( 2 x − 5 ) = 6 x − 15

With a negative multiplier, every sign flips:

− 4 ( 3 x − 7 ) = − 12 x + 28 -4(3x - 7) = -12x + 28 − 4 ( 3 x − 7 ) = − 12 x + 28

A leading minus sign before a parenthesis distributes − 1 -1 − 1 :

8 − ( 3 x − 2 ) = 8 − 3 x + 2 = 10 − 3 x 8 - (3x - 2) = 8 - 3x + 2 = 10 - 3x 8 − ( 3 x − 2 ) = 8 − 3 x + 2 = 10 − 3 x

Producing 8 − 3 x − 2 8 - 3x - 2 8 − 3 x − 2 is among the most common algebra errors on the QAS test.

Identifying Equivalent Expressions

Two expressions are equivalent if they produce the same value for every input.

The Substitution Check

The fastest reliable method: pick a convenient test value and evaluate both.

Is 2 ( 3 x − 4 ) + 5 2(3x - 4) + 5 2 ( 3 x − 4 ) + 5 equivalent to 6 x − 3 6x - 3 6 x − 3 ?

Try x = 2 x = 2 x = 2 :

  • 2 ( 6 − 4 ) + 5 = 2 ( 2 ) + 5 = 9 2(6 - 4) + 5 = 2(2) + 5 = 9 2 ( 6 − 4 ) + 5 = 2 ( 2 ) + 5 = 9
  • 6 ( 2 ) − 3 = 9 6(2) - 3 = 9 6 ( 2 ) − 3 = 9 ✓

Try x = 0 x = 0 x = 0 to confirm:

  • 2 ( 0 − 4 ) + 5 = − 8 + 5 = − 3 2(0 - 4) + 5 = -8 + 5 = -3 2 ( 0 − 4 ) + 5 = − 8 + 5 = − 3
  • 6 ( 0 ) − 3 = − 3 6(0) - 3 = -3 6 ( 0 ) − 3 = − 3 ✓

Equivalent. Use two test values, avoiding 0 and 1 alone, since those can make different expressions coincide by accident.

Algebraic Verification

2 ( 3 x − 4 ) + 5 = 6 x − 8 + 5 = 6 x − 3 2(3x - 4) + 5 = 6x - 8 + 5 = 6x - 3 2 ( 3 x − 4 ) + 5 = 6 x − 8 + 5 = 6 x − 3 ✓

Substitution is faster under test conditions; algebraic expansion is more certain. Use substitution to screen the choices, then expand to confirm the survivor.