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One Variable Equations

Grade 6 · Algebra · Worksheet 1

  1. Tom planted a row of 20 flowers in the garden. Then Tom planted some more flowers to make a total of 23 flowers in the row. How many additional flowers did Tom plant? Answer: ______________
  2. Mia planted a row of 9 flowers in the garden. Then Mia planted some more flowers to make a total of 29 flowers in the row. How many additional flowers did Mia plant? Answer: ______________
  3. x + 2846 = 5001 Answer: ______________
  4. x + 1576 = 2841. Solve for x. Answer: ______________
  5. x + 1523 = 2801. Solve for x. Answer: ______________
  6. Kai and Kai's friend equally shared 35 marbles. Each person received 5 marbles. How many people shared the marbles? Answer: ______________
  7. x + 1577 = 2843 Answer: ______________
  8. Kaia is saving money to buy a new video game. The game costs $71. Kaia already has $33. How much more money does Kaia need to save to buy the game? Answer: ______________
  9. 3(x + 4) - 7 = 20 Answer: ______________
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Answer Key & Explanations

One Variable Equations · Grade 6 · Worksheet 1

  1. Tom planted a row of 20 flowers in the garden. Then Tom planted some more flowers to make a total of 23 flowers in the row. How many additional flowers did Tom plant? Answer: 3 Solution: Let x represent the additional flowers planted. Write the equation: 20 + x = 23. Subtract 20 from both sides: x = 23 - 20.
    Full step-by-step solution

    Step 1: Let x represent the additional flowers planted. Step 2: Write the equation: 20 + x = 23. Step 3: Subtract 20 from both sides: x = 23 - 20. Step 4: Calculate: x = 3. Tom planted 3 more flowers.

  2. Mia planted a row of 9 flowers in the garden. Then Mia planted some more flowers to make a total of 29 flowers in the row. How many additional flowers did Mia plant? Answer: 20 Solution: Let x represent the additional flowers planted. Write the equation: 9 + x = 29. Subtract 9 from both sides: x = 29 - 9.
    Full step-by-step solution

    Step 1: Let x represent the additional flowers planted. Step 2: Write the equation: 9 + x = 29. Step 3: Subtract 9 from both sides: x = 29 - 9. Step 4: Calculate: x = 20. Mia planted 20 more flowers.

  3. x + 2846 = 5001 Answer: 2155 Solution: The equation is x + 2846 = 5001. To isolate x, subtract 2846 from both sides: x + 2846 - 2846 = 5001 - 2846. Simplify: x = 2155.
    Full step-by-step solution

    Step 1: The equation is x + 2846 = 5001. Step 2: To isolate x, subtract 2846 from both sides: x + 2846 - 2846 = 5001 - 2846. Step 3: Simplify: x = 2155. Step 4: Check: 2155 + 2846 = 5001. The answer is 2155.

  4. x + 1576 = 2841. Solve for x. Answer: 1265 Solution: The equation is x + 1576 = 2841. To isolate x, subtract 1576 from both sides of the equation. x + 1576 - 1576 = 2841 - 1576 Simplify: x = 1265 Check: 1265 + 1576 = 2841 ✓ The answer is 1265.
    Full step-by-step solution

    Step 1: The equation is x + 1576 = 2841. Step 2: To isolate x, subtract 1576 from both sides of the equation. Step 3: x + 1576 - 1576 = 2841 - 1576 Step 4: Simplify: x = 1265 Step 5: Check: 1265 + 1576 = 2841 ✓ The answer is 1265.

  5. x + 1523 = 2801. Solve for x. Answer: 1278 Solution: The equation is x + 1523 = 2801. To isolate x, subtract 1523 from both sides of the equation. x + 1523 - 1523 = 2801 - 1523 Simplify: x = 1278 Check: 1278 + 1523 = 2801.
    Full step-by-step solution

    Step 1: The equation is x + 1523 = 2801. Step 2: To isolate x, subtract 1523 from both sides of the equation. Step 3: x + 1523 - 1523 = 2801 - 1523 Step 4: Simplify: x = 1278 Step 5: Check: 1278 + 1523 = 2801. Correct. The answer is 1278.

  6. Kai and Kai's friend equally shared 35 marbles. Each person received 5 marbles. How many people shared the marbles? Answer: 7 Solution: Let x represent the number of people sharing. Write the equation: x × 5 = 35. Divide both sides by 5: x = 35 ÷ 5.
    Full step-by-step solution

    Step 1: Let x represent the number of people sharing. Step 2: Write the equation: x × 5 = 35. Step 3: Divide both sides by 5: x = 35 ÷ 5. Step 4: Calculate: x = 7. There were 7 people sharing the marbles.

  7. x + 1577 = 2843 Answer: 1266 Solution: The equation is x + 1577 = 2843. To isolate x, subtract 1577 from both sides of the equation. x + 1577 - 1577 = 2843 - 1577 Simplify: x = 1266 Check: 1266 + 1577 = 2843.
    Full step-by-step solution

    Step 1: The equation is x + 1577 = 2843. Step 2: To isolate x, subtract 1577 from both sides of the equation. Step 3: x + 1577 - 1577 = 2843 - 1577 Step 4: Simplify: x = 1266 Step 5: Check: 1266 + 1577 = 2843. Correct. The answer is 1266.

  8. Kaia is saving money to buy a new video game. The game costs $71. Kaia already has $33. How much more money does Kaia need to save to buy the game? Answer: 38 Solution: Let x represent the additional money needed. Write the equation: 33 + x = 71. Subtract 33 from both sides: x = 71 - 33.
    Full step-by-step solution

    Step 1: Let x represent the additional money needed. Step 2: Write the equation: 33 + x = 71. Step 3: Subtract 33 from both sides: x = 71 - 33. Step 4: Calculate: x = 38. Kaia needs to save $38 more.

  9. 3(x + 4) - 7 = 20 Answer: 5 Solution: 3(x + 4) - 7 = 20 Add 7 to both sides This removes the -7 on the left. 3(x + 4) - 7 + 7 = 20 + 7 3(x + 4) = 27 Divide both sides by 3 This isolates the term (x + 4).
    Full step-by-step solution

    Let's solve the equation step by step. We start with: 3(x + 4) - 7 = 20 **Step 1: Add 7 to both sides** This removes the -7 on the left. 3(x + 4) - 7 + 7 = 20 + 7 3(x + 4) = 27 **Step 2: Divide both sides by 3** This isolates the term (x + 4). [3(x + 4)] / 3 = 27 / 3 x + 4 = 9 **Step 3: Subtract 4 from both sides** This isolates x. x + 4 - 4 = 9 - 4 x = 5 **Final check:** Plug x = 5 into the original equation: 3(5 + 4) - 7 = 3(9) - 7 = 27 - 7 = 20 ✓ The solution is x = 5.