Unit 4 Workbook — Expressions & Equations

Practice exponents, order of operations, writing & evaluating expressions, one-step equations, and inequalities — solve each one right here and check yourself.

🟢 Easy

Problem 1 · Exponents

Evaluate: 4² = ?

💡 Hint

The little 2 means "squared" — how many 4's do you multiply together?

4² means use 4 as a factor 2 times: 4 × 4 = 16. Squaring is a number times itself — the area of a 4-by-4 square — which is why it is 16, not 4 × 2 = 8. Answer: 16

Problem 2 · Exponents

Evaluate: 2³ = ?

💡 Hint

Does the 3 tell you to multiply 2 by 3, or to use three 2's?

2³ means use 2 as a factor 3 times: 2 × 2 × 2 = 8 (not 2 × 3). The exponent counts how many copies of the base you multiply — it is a counter, not a multiplier, which is the classic trap. Answer: 8

Problem 3 · Order of operations

Evaluate: 3 + 4 × 2 = ?

💡 Hint

PEMDAS — which do you do first, the multiply or the add?

PEMDAS: multiply before adding.

Multiply: 4 × 2 = 8 → then add: 3 + 8 = 11 (not 14). Multiplication outranks addition, so the 4 and 2 join first; going left-to-right instead would wrongly give 14. Answer: 11

Problem 4 · Writing expressions

Which expression means "8 more than a number n"?

8n n + 8 n − 8 8 − n

💡 Hint

"More than" — does that add to n or take away from it?

"More than" means add. 8 more than n is n + 8. Since adding can be done in either order, n + 8 and 8 + n mean the same thing — the trap answers 8n and 8 − n change the operation entirely. Answer: n + 8

Problem 5 · Evaluating expressions

Evaluate x + 6 when x = 9.

💡 Hint

Swap the x for its value, 9 — then just add.

Replace x with 9: 9 + 6 = 15. Evaluating means substituting the variable's value and then doing the arithmetic, so x simply becomes 9 here. Answer: 15

Problem 6 · One-step equations

Solve: x + 5 = 12. x = ?

💡 Hint

What operation undoes adding 5? Do it to both sides to keep the scale balanced.

5 is added to x, so subtract 5 from both sides.

x + 5 − 5 = 12 − 5 → x = 7. Check: 7 + 5 = 12 ✓. Subtraction is the inverse of addition, and doing it to both sides keeps the equation balanced so the answer stays valid. Answer: 7

🟡 Medium

Problem 7 · Exponents

Evaluate: 10³ = ?

💡 Hint

Three 10's multiplied — what does each factor of 10 do to the number of zeros?

10 × 10 × 10 = 1,000. Each factor of 10 tacks on one zero, so three 10's give exactly three zeros — that pattern is why powers of 10 are so quick to write. Answer: 1000

Problem 8 · Order of operations

Evaluate: 2 + 3² × 4 = ?

💡 Hint

In PEMDAS, which comes first here — the exponent, the multiply, or the add?

PEMDAS: exponent, then multiply, then add.

Exponent: 3² = 9 → multiply: 9 × 4 = 36 → add: 2 + 36 = 38. Following the ranking keeps the lone 2 out of the multiplication until the very end, which is what makes the order matter. Answer: 38

Problem 9 · Writing expressions

Which expression means "the product of 6 and a number m, then decreased by 2"?

6 + m − 2 6m − 2 2 − 6m 6(m − 2)

💡 Hint

"Product of 6 and m" then "decreased by 2" — which operation happens last?

"Product of 6 and m" is 6m; "decreased by 2" means subtract 2: 6m − 2. The wording builds the product first and only then removes 2, so the subtraction stays outside — 6(m − 2) would wrongly subtract before multiplying. Answer: 6m − 2

Problem 10 · Evaluating expressions

Evaluate 3x − 4 when x = 5.

💡 Hint

After replacing x with 5, which do you do first — multiply or subtract?

Replace x with 5: 3 × 5 − 4 = 15 − 4 = 11. By PEMDAS the 3x (multiplication) happens before the −4, so the 15 forms first — subtracting first would give the wrong value. Answer: 11

Problem 11 · One-step equations

Solve: 4x = 28. x = ?

💡 Hint

4x means 4 × x — what operation undoes multiplying by 4?

x is multiplied by 4, so divide both sides by 4.

4x ÷ 4 = 28 ÷ 4 → x = 7. Check: 4 × 7 = 28 ✓. Division is the inverse of multiplication, so it splits 28 back into the 4 equal groups that built it. Answer: 7

Problem 12 · One-step equations

Solve: y ÷ 3 = 9. y = ?

💡 Hint

What operation undoes dividing by 3?

y is divided by 3, so multiply both sides by 3.

y ÷ 3 × 3 = 9 × 3 → y = 27. Check: 27 ÷ 3 = 9 ✓. Multiplying rebuilds the whole that was cut into 3 equal parts, so it cancels the division. Answer: 27

🔴 Hard

Problem 13 · Order of operations

Evaluate: (2³ + 4) × 2 = ?

💡 Hint

What must you finish inside the parentheses before you multiply by 2?

Do inside the parentheses first (exponent, then add), then multiply.

2³ = 8 → 8 + 4 = 12 → 12 × 2 = 24. Parentheses act like a wrapper that must be fully simplified to a single number (12) before it can be multiplied. Answer: 24

Problem 14 · Order of operations

Evaluate: 4² − 2 × (6 − 1) = ?

💡 Hint

Work PEMDAS in order — parentheses, then the exponent, then the multiply, then the subtract.

Parentheses → exponent → multiply → subtract.

Parentheses: 6 − 1 = 5 → exponent: 4² = 16 → multiply: 2 × 5 = 10 → subtract: 16 − 10 = 6. Handling each rank in turn keeps the subtraction for last, so the 16 and the 10 are both fully built before they meet. Answer: 6

Problem 15 · Evaluating expressions

Evaluate 2a² + 3 when a = 4.

💡 Hint

Square the 4 before you double it — does the exponent or the multiply come first?

Exponent first, then multiply, then add.

Replace a with 4: 2 × 4² + 3 → 4² = 16 → 2 × 16 = 32 → 32 + 3 = 35. The exponent applies only to the a, so you square 4 first; doubling before squaring (giving 8² = 64) is the common slip. Answer: 35

Problem 16 · One-step equations

Solve: 7x = 84. x = ?

💡 Hint

What operation undoes multiplying by 7?

x is multiplied by 7, so divide both sides by 7.

7x ÷ 7 = 84 ÷ 7 → x = 12. Check: 7 × 12 = 84 ✓. Dividing both sides by 7 is the inverse that isolates x while keeping the equation balanced. Answer: 12

Problem 17 · Inequalities

Which inequality means "a number n is at most 7"?

n > 7 n < 7 n ≥ 7 n ≤ 7

💡 Hint

"At most 7" — can n equal exactly 7? Which symbol includes "or equal to"?

"At most 7" means 7 or less — it can equal 7 but no more. That is n ≤ 7 (less than or equal to). The underline folds 7 itself into the answer, and "at most" caps the top end rather than the bottom. Answer: n ≤ 7

Problem 18 · Graphing inequalities

On a number line, there is an open circle at 3 with the arrow pointing right. Which inequality does this graph show?

x ≥ 3 x > 3 x < 3 x ≤ 3

💡 Hint

Open circle = included or not? Arrow pointing right = bigger or smaller values?

An open circle means 3 is not included (so no "equal to"). The arrow pointing right means the values are greater than 3. Together: x > 3. The graph encodes two facts at once — the hollow dot rules out 3, and the rightward arrow points toward everything larger. Answer: x > 3

⚡ Nice work. You practiced exponents, PEMDAS, writing & evaluating expressions, solving one-step equations (+ − × ÷), and reading/writing inequalities. Use Show solution on any you missed, then Reset to try again from a clean slate.

Grounded in CA CCSS-M, Grade 6 · 6.EE, California Department of Education. Image generated with Gemini Nano Banana Pro.