Solve linear equations

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    amara.reedAmara · Maths Made Clear

    • 🎯 Try it

    Single choice

    Solve 4x−3=94x - 3 = 9.

    x+4=11x + 4 = 11: x=7x = 7. Check: 7+4=117 + 4 = 11.

    ⏱️ Practice timer
    05:00

    🔎 Worked example

    Equation⇅
    Operation on both sides⇅
    3x+5=203x + 5 = 20
    Subtract 5
    3x=153x = 15
    Divide by 3
    x=5x = 5
    Substitute: 3×5+5=203 \times 5 + 5 = 20

    Treat both sides as a balance: apply the same operation to each. Check the solution in the original equation.

    ✏️ Practice

  • 1.
    Solve x+8=15x + 8 = 15. Check by substitution.
  • 2.
    Solve 5x=305x = 30. Check by substitution.
  • 3.
    Solve 2x+6=182x + 6 = 18. Show both operations.
  • 4.
    Solve 5x−7=185x - 7 = 18. Explain your first operation.
  • 5.
    Solve 4(x+2)=144(x + 2) = 14. Compare it with 4x+2=144x + 2 = 14.
  • 6.
    Jo writes 3x+4=193x + 4 = 19, then 3x=233x = 23. Find and correct the first error.

    • 💭 Your answer

    Single choice

    A learner changes 2x+6=102x + 6 = 10 into 2x=102x = 10. What is missing?

    ✅ Quick check

    Single choice

    Solve 3x+2=143x + 2 = 14 and choose the checked result.

    🔑 Answers

    🔑 Practice answers

  • 1.
    x=7x = 7: subtract 8; 7+8=157 + 8 = 15.
  • 2.
    x=6x = 6: divide by 5; 5×6=305 \times 6 = 30.
  • 3.
    Subtract 6: 2x=122x = 12. Divide by 2: x=6x = 6. Check: 12+6=1812 + 6 = 18.
  • 4.
    Add 7: 5x=255x = 25. Divide by 5: x=5x = 5. Check: 25−7=1825 - 7 = 18.
  • 5.
    Divide by 4: x+2=3.5x + 2 = 3.5. Subtract 2: x=1.5x = 1.5. Check: 4×3.5=144 \times 3.5 = 14. Without brackets, 4x+2=144x + 2 = 14 gives x=3x = 3.
  • 6.
    Subtract 4 from both sides: 3x=153x = 15, so x=5x = 5. Jo added 4 on the right while removing it on the left.

    • 💡 Hint and challenge

    💡 Hint: Use positive integer solutions and show one operation per line.

    ⭐ Challenge: Solve 3x+4=x+143x + 4 = x + 14; explain why subtracting xx from both sides is allowed.

    🔎 Challenge answer

    3x+4=x+142x+4=142x=10x=5\begin{aligned} 3x + 4 &= x + 14 \\ 2x + 4 &= 14 \\ 2x &= 10 \\ x &= 5 \end{aligned}

    Subtracting xx removes the same quantity from each side. Check: 19=1919 = 19.

    ➡️ Next lesson

    Algebra practice with worked corrections.

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    Comments2
    Created by
  • AC
    amara.reedAmara · Maths Made Clear