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|1010a−8-8|=7878

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Full solution

Q. |1010a−8-8|=7878
  1. Understand absolute value: First, let's understand the absolute value. The equation ∣10a−8∣=78|10a-8|=78 means that 10a−810a-8 is either 7878 or −78-78.
  2. Solve for 10a=7810a=78: Now, let's solve for 10a−8=7810a-8=78. Add 88 to both sides to isolate the term with the variable. 10a=78+810a = 78 + 8 10a=8610a = 86
  3. Calculate a=8.6a=8.6: Next, divide both sides by 1010 to solve for aa.\newlinea=8610a = \frac{86}{10}\newlinea=8.6a = 8.6
  4. Consider other possibility: Now, let's consider the other possibility, 10a−8=−7810a-8=-78. Add 88 to both sides. 10a=−78+810a = -78 + 8 10a=−7010a = -70
  5. Solve for a=−7a=-7: Divide both sides by 1010 to solve for aa.\newlinea=−7010a = \frac{-70}{10}\newlinea=−7a = -7

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