Algebra 1 Structure of Algebraic Expressions Worksheet Solutions (PDF)

Algebra 1 math worksheet solutions: Structure of Algebraic Expressions – Maths PDF

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This algebra 1 expressions answers for Algebra 1 covers structure of algebraic expressions (Common Core A-SSE.A.1a, A-SSE.A.1b), with a free PDF to print.

Use this key to check your work on the expressions worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer differs, find the first line where your work and the key disagree, then redo the problem from there without looking.

Algebra 1 · Common Core State Standards: A-SSE.A.1a, A-SSE.A.1b

Algebra 1 expressions answers: exercises 1 to 10

Exercise 1 – Coefficient of x

The term with $x$ is $6x$, so the number multiplying $x$ is 6.

Exercise 2 – Count the terms

Terms are separated by + and – signs: $4a^{2}$, $-3a$, and $8$.

3 terms

Exercise 3 – Name the constant

The constant term has no variable. In $2x^{2} – 9x + 14$ it is the last term.

Exercise 4 – Factors in a product

A product is made of factors that are multiplied. Here $5$ is multiplied by the group $(x – 2)$.

$5$ and $(x – 2)$

Exercise 5 – Evaluate an expression

Substitute $-2$ for $x$: $3(-2)^{2} – 2(-2) + 5$.

Square first: $3(4) + 4 + 5 = 12 + 4 + 5$.

$21$

Exercise 6 – Pick the like terms

Like terms have the same variable part. $5x$ and $-2x$ both have $x$ to the first power.

$4x^{2}$ has a different exponent, and $3y$ has a different variable.

$5x$ and $-2x$

Exercise 7 – Combine like terms

Like terms are combined separately.

Group like terms: $(8x – 5x) + (3 + 9)$.

Combine: $3x + 12$.

$3x + 12$

Exercise 8 – Distribute a number

Multiply 4 by each term inside: $4 \cdot 3x = 12x$ and $4 \cdot (-5) = -20$.

$12x – 20$

Exercise 9 – Distribute a negative

Multiply each term by $-2$: $(-2)(x) = -2x$ and $(-2)(-6) = +12$.

$-2x + 12$

Exercise 10 – Distribute and combine

Distribute: $6x + 3 + 4x – 7$.

Combine like terms: $(6x + 4x) + (3 – 7)$.

$10x – 4$

Exercises 11 and up

Exercise 11 – Subtract an expression

Subtracting changes the sign of every term in the second group: $7x + 5 – 3x + 2$.

Combine: $(7x – 3x) + (5 + 2)$.

$4x + 7$

Exercise 12 – One quantity

Both terms contain the factor $(x – 3)$. Add the coefficients: $2 + 5 = 7$.

$7(x – 3)$

Exercise 13 – Taxi fare meaning

$2.25$ is the coefficient of $m$: the cost for each mile. The table shows it, since the fare rises $2.25 per mile ($\$5.75 \to \$8.00$).

$3.50$ is the constant: a fixed charge paid before any miles.

$2.25 per mile; $3.50 starting charge

Exercise 14 – Write an expression

3 times a number is $3n$. Taking away 5 gives $3n – 5$.

$3n – 5$

Exercise 15 – Gym membership

Rate $\$18$ per month times $m$ months, plus the one-time fee: $18m + 25$.

Substitute $m = 6$: $18(6) + 25 = 108 + 25 = 133$.

$18m + 25$; $133

Exercise 16 – Perimeter

Perimeter of the garden.

Perimeter is $2(3x + 2) + 2(x + 5)$.

Distribute: $6x + 4 + 2x + 10$, which simplifies to $8x + 14$.

For $x = 4$: $8(4) + 14 = 46$ feet.

$8x + 14$; 46 feet

Exercise 17 – Bake sale

Money is $1.50c + 2.25b$.

For $c = 24$ and $b = 18$: $1.50(24) + 2.25(18) = 36 + 40.50 = 76.50$.

The term $2.25b$ is the money earned from brownies alone.

$1.50c + 2.25b$; $76.50

Exercise 18 – Sale price

$0.85p$ is 0.85 times $p$. Paying 85% of the price means a 15% discount, and the 4 is a shipping charge.

For $p = 60$: $0.85(60) + 4 = 51 + 4 = 55$.

15% discount; $55

Exercise 19 – Patio area

Garden parts $4x$ and 28; patio $x^{2}$.

Garden area: $4(x + 7) = 4x + 28$. Patio area: $x \cdot x = x^{2}$.

Total: $x^{2} + 4x + 28$.

For $x = 5$: $25 + 20 + 28 = 73$.

$x^{2} + 4x + 28$; 73 square feet

Exercise 20 – Compare two plans

$(4 + 2.5m) – (1.5 + 3m) = 4 + 2.5m – 1.5 – 3m$.

Combine like terms: $2.5 – 0.5m$.

For $m = 3$: $2.5 – 0.5(3) = 2.5 – 1.5 = 1$, so A costs $1 more.

$2.5 – 0.5m$; $1

Exercise 21 – Fundraiser tickets

Distribute: $3(2s + 3a) = 6s + 9a$, so the expressions are equivalent.

Substitute: $6(40) + 9(25) = 240 + 225 = 465$.

Equivalent; $465

Key facts behind this algebra 1 expressions answers

Key facts

Terms are separated by + and – signs, and each term keeps its own sign.
A coefficient multiplies a variable; a constant has no variable.
Like terms have the same variable part and can be combined by adding coefficients.
A grouped expression such as (x + 3) can be treated as one factor.
In a model, a coefficient is often a rate and a constant is a starting amount.

How to use this algebra 1 expressions answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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