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Modulus equation solution

CMAT 2018 · Quantitative Techniques & Data Interpretation · Medium · Algebra

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Find the value of aa, if: ∣2a−3∣=3a+2|2a - 3| = 3a + 2

  1. A.

    1/5

  2. B.

    0

  3. C.

    -5

  4. D.

    -1/5

Answer

A

Explanation

Case 1: 2a−3≥0  ⟹  a≥1.52a - 3 \ge 0 \implies a \ge 1.5. 2a−3=3a+2  ⟹  a=−52a - 3 = 3a + 2 \implies a = -5 (Invalid since −5<1.5-5 < 1.5).

Case 2: 2a−3<0  ⟹  a<1.52a - 3 < 0 \implies a < 1.5. −(2a−3)=3a+2  ⟹  −2a+3=3a+2  ⟹  5a=1  ⟹  a=1/5-(2a - 3) = 3a + 2 \implies -2a + 3 = 3a + 2 \implies 5a = 1 \implies a = 1/5. Since 1/5<1.51/5 < 1.5, a=1/5a = 1/5 is valid.

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