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10 (a) Solve the inequality - OCR - GCSE Maths - Question 10 - 2017 - Paper 1

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10 (a) Solve the inequality. 3x - 2 > 10 (b) Solve. 6x + 2 = 5 - 4x

Worked Solution & Example Answer:10 (a) Solve the inequality - OCR - GCSE Maths - Question 10 - 2017 - Paper 1

Step 1

Solve the inequality.

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Answer

To solve the inequality 3x−2>103x - 2 > 10, we first isolate the variable xx:

  1. Add 2 to both sides:

    3x−2+2>10+23x - 2 + 2 > 10 + 2

    This simplifies to:

    3x>123x > 12

  2. Now, divide both sides by 3:

    x>123x > \frac{12}{3}

    Thus, we have:

    x>4x > 4

Step 2

Solve.

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Answer

For the equation 6x+2=5−4x6x + 2 = 5 - 4x, we will rearrange it:

  1. First, add 4x4x to both sides:

    6x+4x+2=56x + 4x + 2 = 5

    This simplifies to:

    10x+2=510x + 2 = 5

  2. Next, subtract 2 from both sides:

    10x=5−210x = 5 - 2

    Which gives:

    10x=310x = 3

  3. Finally, divide both sides by 10:

    x=310x = \frac{3}{10}

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