Fix algebra mistakes

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    amara.reedAmara · Maths Made Clear

    • 🎯 Try it

    Single choice

    Expand −2(x−4)-2(x - 4).

    📝 Start with the mistake

    Work on paper; compare each line with the explanation before trying the next problem.

    Distribution: A learner writes 3(x+4)=3x+43(x + 4) = 3x + 4. Both terms inside the bracket must be multiplied: 3x+123x + 12. Try 2(x−5)2(x - 5), then −2(x+3)-2(x + 3). Answers: 2x−102x - 10; −2x−6-2x - 6.

    Combining terms: 3x+2x=5x3x + 2x = 5x, but 3x+23x + 2 cannot become 5x5x. Only like terms combine. Simplify 4a+3−a+54a + 3 - a + 5: 3a+83a + 8.

    Equation balance: For 5x−7=185x - 7 = 18, add 7 to both sides, then divide by 5. x=5x = 5; substitution gives 25−7=1825 - 7 = 18.

    Sign check: −3x=12-3x = 12 gives x=−4x = -4. Dividing by a negative changes the sign of a positive quotient.

    ✏️ Mixed practice

  • 1.
    Expand 4(2x−3)4(2x - 3).
  • 2.
    Simplify 7y−2+3y+67y - 2 + 3y + 6.
  • 3.
    Solve 2x+9=12x + 9 = 1. Check the sign by substitution.
  • 4.
    Solve 3x+2=x+103x + 2 = x + 10.
  • 5.
    A learner writes −2(x−3)=−2x−6-2(x - 3) = -2x - 6. Identify the first error.
  • 6.
    Solve 5−2x=115 - 2x = 11, then check in the original equation.

    • 🔑 Worked corrections

  • 1.
    8x−128x - 12: distribute 4 to both terms.
  • 2.
    10y+410y + 4: combine yy terms separately from constants.
  • 3.
    x=−4x = -4: subtract 9 to get 2x=−82x = -8; 2(−4)+9=12(-4) + 9 = 1.
  • 4.
    x=4x = 4: subtract xx and 2 from both sides to get 2x=82x = 8.
  • 5.
    The second product is positive: (−2)(−3)=6(-2)(-3) = 6, so −2x+6-2x + 6.
  • 6.
    x=−3x = -3: subtract 5, then divide by −2-2; 5−2(−3)=115 - 2(-3) = 11.

    • ✅ Check your understanding

    Single choice

    Solve 4x+1=134x + 1 = 13.

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    Created by
  • AC
    amara.reedAmara · Maths Made Clear