Grade: Grade 6 Subject: Mathematics Unit: Expressions & Equations SAT: Algebra ACT: Math

Guided Practice

Work through expressions and equations problems with step-by-step hints and immediate feedback to build your confidence.

Your Progress

0 of 10 problems completed

Part 1: Writing Expressions

Practice translating words into algebraic expressions. Use the hints if you need help!

Guided Problem 1

Write an algebraic expression for: "six more than a number"
Hint:

"More than" tells you to use addition. The phrase means you start with a number (use a variable like n) and add 6 to it.

Guided Problem 2

Write an algebraic expression for: "the product of 5 and a number"
Hint:

"Product" means multiplication. When you multiply a number by a variable, write the number first: 5n (not n5).

Guided Problem 3

Write an algebraic expression for: "8 less than a number"
Hint:

Careful! "Less than" flips the order. "8 less than n" means start with n and subtract 8. The answer is n - 8, NOT 8 - n.

Guided Problem 4

Write an algebraic expression for: "twice a number, plus 7"
Hint:

"Twice" means multiply by 2. First write 2n (twice a number), then add 7. The expression is 2n + 7.

Guided Problem 5

Write an algebraic expression for: "a number divided by 4"
Hint:

"Divided by" means division. A number (n) divided by 4 is written as n / 4 or n/4.

Part 2: Solving Equations

Practice solving one-step equations. Remember to use inverse operations!

Guided Problem 6

Solve: x + 9 = 17
Hint:

9 is being added to x. To undo addition, use subtraction. Subtract 9 from both sides: x + 9 - 9 = 17 - 9.

Guided Problem 7

Solve: n - 15 = 22
Hint:

15 is being subtracted from n. To undo subtraction, use addition. Add 15 to both sides: n - 15 + 15 = 22 + 15.

Guided Problem 8

Solve: 6y = 42
Hint:

y is being multiplied by 6. To undo multiplication, use division. Divide both sides by 6: 6y / 6 = 42 / 6.

Guided Problem 9

Solve: m / 5 = 9
Hint:

m is being divided by 5. To undo division, use multiplication. Multiply both sides by 5: (m / 5) x 5 = 9 x 5.

Guided Problem 10

Solve: p + 27 = 50
Hint:

27 is being added to p. To undo addition, subtract 27 from both sides: p + 27 - 27 = 50 - 27.

Quick Practice: Multiple Choice

Test your skills with these additional problems.

Problem 11

What is the algebraic expression for "three times a number, decreased by 4"?

Problem 12

Solve: 8k = 72

Next Steps

What You Practiced:

  • Writing expressions from word phrases using key operation words
  • Handling "less than" and "subtracted from" (they flip the order!)
  • Solving one-step equations using inverse operations
  • Checking your work by substituting back
Keep Practicing! The more you practice, the faster and more accurate you'll become. Try creating your own word phrases and translating them!