Name:
Date:
Form (A / B):
How to use this worksheet. Every equation is a small puzzle: your job is to get
x by itself on one side. The trick is always the same — do the
opposite operation.
- Write your answer on each line. Show your work in the margin if it helps.
- For a (circle one) question, circle the choice you believe is correct.
- Each part has a Clarify hint. Try the part first; read the hint only if you get stuck. It gives you a method, never the answer.
FORM A
Practice Set A
PART 1
Opposites
Write the opposite operation.
1.Plus 5 Opposite:
2.Minus 3 Opposite:
3.Multiply by 2 Opposite:
4.Divide by 4 Opposite:
5.Minus 10 Opposite:
Clarify — Every operation has an opposite that undoes it. Adding and subtracting are a pair; multiplying and dividing are a pair. Ask yourself: "What would cancel this out?"
PART 2
Solve for X (Addition / Subtraction)
Get X by itself.
6.x + 2 = 5 Answer: x =
7.x − 3 = 4 Answer: x =
8.x + 5 = 10 Answer: x =
9.x − 1 = 9 Answer: x =
10.4 + x = 8 Answer: x =
Clarify — To get x alone, do the opposite operation to both sides. If a number is added to x, subtract that same number from both sides; if it is subtracted, add it to both sides.
PART 3
Solve for X (Multiplication / Division)
Get X by itself.
11.2x = 10 (Hint: Divide by 2) Answer: x =
12.3x = 9 Answer: x =
13.5x = 25 Answer: x =
14.x ÷ 2 = 4 (Hint: Multiply by 2) Answer: x =
15.4x = 8 Answer: x =
Clarify — When x is multiplied by a number, undo it by dividing both sides by that number. When x is divided by a number, undo it by multiplying both sides. Always the opposite.
PART 4
Checking Your Work
Plug the number in to see if it works.
16.Is x = 3 the answer for: x + 2 = 5? (circle one): Yes | No
17.Is x = 4 the answer for: 2x = 10? (circle one): Yes | No
18.Solve: x + 10 = 20 Answer:
19.Solve: x − 5 = 0 Answer:
20.Solve: 2x = 4 Answer:
Clarify — To check, put the given number in place of x and work out both sides. If the two sides come out equal, the number fits; if they do not, it does not. Do the arithmetic before you circle.
FORM B
Practice Set B
PART 1
Opposites
Write the opposite operation.
1.Plus 7 Opposite:
2.Minus 4 Opposite:
3.Multiply by 3 Opposite:
4.Divide by 5 Opposite:
5.Minus 8 Opposite:
Clarify — Every operation has an opposite that undoes it. Adding and subtracting are a pair; multiplying and dividing are a pair. Ask yourself: "What would cancel this out?"
PART 2
Solve for X (Addition / Subtraction)
Get X by itself.
6.x + 3 = 7 Answer: x =
7.x − 2 = 5 Answer: x =
8.x + 4 = 9 Answer: x =
9.x − 5 = 5 Answer: x =
10.2 + x = 6 Answer: x =
Clarify — To get x alone, do the opposite operation to both sides. If a number is added to x, subtract that same number from both sides; if it is subtracted, add it to both sides.
PART 3
Solve for X (Multiplication / Division)
Get X by itself.
11.2x = 12 (Hint: Divide by 2) Answer: x =
12.3x = 12 Answer: x =
13.5x = 10 Answer: x =
14.x ÷ 2 = 3 (Hint: Multiply by 2) Answer: x =
15.4x = 16 Answer: x =
Clarify — When x is multiplied by a number, undo it by dividing both sides by that number. When x is divided by a number, undo it by multiplying both sides. Always the opposite.
PART 4
Checking Your Work
Plug the number in to see if it works.
16.Is x = 5 the answer for: x + 3 = 8? (circle one): Yes | No
17.Is x = 3 the answer for: 2x = 8? (circle one): Yes | No
18.Solve: x + 5 = 15 Answer:
19.Solve: x − 2 = 0 Answer:
20.Solve: 3x = 6 Answer:
Clarify — To check, put the given number in place of x and work out both sides. If the two sides come out equal, the number fits; if they do not, it does not. Do the arithmetic before you circle.
FOR MENTOR USE — WORK THROUGH THIS TOGETHER
Mentor Guide
How to coach one-step equations without handing over the answers
1. What this worksheet builds
It teaches one big idea from four angles: to solve an equation, you undo the operation that is attached to x. Part 1 names the opposite operations, Parts 2 and 3 apply them, and Part 4 checks the result. The two forms (A and B) are parallel — same skills, different numbers — so a student can retry the skill fresh, or one form can be practice and the other a check-in.
2. Run it with gradual release: I do → we do → you do
- I do: Solve one Part 2 equation out loud, saying each move — "x has 2 added to it, so I subtract 2 from both sides."
- We do: Do the next few together; you narrate the plan, the student does the arithmetic.
- You do: Let them work a full part alone, stepping in only when they reach a Clarify hint.
3. Using the Clarify hints
Let the student attempt each part first; read the Clarify box only if they stall. The hints coach method ("do the opposite to both sides," "cancel it out"), never a numeric answer. As a next step, ask the student to say the hint back to you before they read it — that is the strategy becoming their own.
4. Common stumbles & how to unstick them
- "4 + x" or "2 + x" throws them. Remind them addition can be flipped — it is the same as "x + 4." The plan does not change.
- They pick the operation in the equation instead of its opposite. Point back to Part 1 and ask, "What undoes this?"
- Division looks scary. For "x ÷ 2 = 4," act it out with counters: x split into groups of that size equals the answer, so multiply back.
5. Reviewing it together — without an answer key
- You do not need a key: have the student check every answer by substitution (Part 4's skill). Put the number back in for x — if both sides match, it is right. This makes the student the checker.
- For a "circle one" item, ask them to prove it by working the arithmetic aloud rather than just defending the circle.
- Praise a specific strength first ("you undid both sides cleanly"), then pick one pattern to fix. Compare each form to the student's own earlier work — progress is the measure.