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One Variable Equations

Grade 6 · Algebra · Worksheet 1

  1. 3(x + 4) - 7 = 20 Answer: ______________
  2. Emma draws a rectangle on a grid. The length of the rectangle is 25 cm. If the perimeter of the rectangle is 80 cm, what is the width of the rectangle in centimeters? Answer: ______________
  3. x + 1621 = 2806 Answer: ______________
  4. x + 1272 = 2847 Answer: ______________
  5. Kai and Kai's friend equally shared 35 marbles. Each person received 5 marbles. How many people shared the marbles? Answer: ______________
  6. x + 1576 = 2841. Solve for x. Answer: ______________
  7. 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: ______________
  8. Aisha is designing a rectangular community garden for her school. The length of the garden is 8 meters more than its width. If the perimeter of the garden is 64 meters, what is the width of the garden in meters? Answer: ______________
  9. Noah is designing a scale model of a solar system for his science project. The actual distance from Earth to Mars is approximately 225 million kilometers. If Noah's model uses a scale where 1 centimeter represents 15 million kilometers, how many centimeters apart should he place the Earth and Mars models in his display? Answer: ______________
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Answer Key & Explanations

One Variable Equations · Grade 6 · Worksheet 1

  1. 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.

  2. Emma draws a rectangle on a grid. The length of the rectangle is 25 cm. If the perimeter of the rectangle is 80 cm, what is the width of the rectangle in centimeters? Answer: 15 Solution: The formula for the perimeter of a rectangle is P = 2 × (length + width). Substitute the given values: 80 = 2 × (25 + w), where w is the width. Divide both sides by 2: 80 ÷ 2 = 2 × (25 + w) ÷ 2 → 40 = 25 + w.
    Full step-by-step solution

    Step 1: The formula for the perimeter of a rectangle is P = 2 × (length + width). Step 2: Substitute the given values: 80 = 2 × (25 + w), where w is the width. Step 3: Divide both sides by 2: 80 ÷ 2 = 2 × (25 + w) ÷ 2 → 40 = 25 + w. Step 4: Subtract 25 from both sides: 40 - 25 = 25 + w - 25 → 15 = w. The width of the rectangle is 15 cm.

  3. x + 1621 = 2806 Answer: 1185 Solution: The equation is x + 1621 = 2806. To isolate x, subtract 1621 from both sides of the equation. x + 1621 - 1621 = 2806 - 1621 Simplify: x = 1185 Check: 1185 + 1621 = 2806.
    Full step-by-step solution

    Step 1: The equation is x + 1621 = 2806. Step 2: To isolate x, subtract 1621 from both sides of the equation. Step 3: x + 1621 - 1621 = 2806 - 1621 Step 4: Simplify: x = 1185 Step 5: Check: 1185 + 1621 = 2806. Correct. The answer is 1185.

  4. x + 1272 = 2847 Answer: 1575 Solution: The equation is x + 1272 = 2847. To isolate x, subtract 1272 from both sides of the equation. x + 1272 - 1272 = 2847 - 1272 Simplify: x = 1575 Check: 1575 + 1272 = 2847 ✓ The answer is 1575.
    Full step-by-step solution

    Step 1: The equation is x + 1272 = 2847. Step 2: To isolate x, subtract 1272 from both sides of the equation. Step 3: x + 1272 - 1272 = 2847 - 1272 Step 4: Simplify: x = 1575 Step 5: Check: 1575 + 1272 = 2847 ✓ The answer is 1575.

  5. 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.

  6. 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.

  7. 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.

  8. Aisha is designing a rectangular community garden for her school. The length of the garden is 8 meters more than its width. If the perimeter of the garden is 64 meters, what is the width of the garden in meters? Answer: 12 Solution: Let w represent the width of the garden in meters. Since the length is 8 meters more than the width, the length is w + 8 meters. The formula for perimeter of a rectangle is P = 2 × length + 2 × width.
    Full step-by-step solution

    Step 1: Let w represent the width of the garden in meters. Step 2: Since the length is 8 meters more than the width, the length is w + 8 meters. Step 3: The formula for perimeter of a rectangle is P = 2 × length + 2 × width. Step 4: Substitute the known values: 64 = 2(w + 8) + 2w Step 5: Expand the equation: 64 = 2w + 16 + 2w Step 6: Combine like terms: 64 = 4w + 16 Step 7: Subtract 16 from both sides: 64 - 16 = 4w + 16 - 16 Step 8: Simplify: 48 = 4w Step 9: Divide both sides by 4: 48 ÷ 4 = 4w ÷ 4 Step 10: Simplify: 12 = w The width of the garden is 12 meters.

  9. Noah is designing a scale model of a solar system for his science project. The actual distance from Earth to Mars is approximately 225 million kilometers. If Noah's model uses a scale where 1 centimeter represents 15 million kilometers, how many centimeters apart should he place the Earth and Mars models in his display? Answer: 15 Solution: Identify the actual distance: 225 million kilometers Identify the scale: 1 centimeter = 15 million kilometers Set up the equation: model distance = actual distance ÷ scale factor Calculate: 225 ÷ 15 = 15 The Earth and Mars models should be 15 centimeters apart in Noah's display.
    Full step-by-step solution

    Step 1: Identify the actual distance: 225 million kilometers Step 2: Identify the scale: 1 centimeter = 15 million kilometers Step 3: Set up the equation: model distance = actual distance ÷ scale factor Step 4: Calculate: 225 ÷ 15 = 15 Step 5: The Earth and Mars models should be 15 centimeters apart in Noah's display.