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You have 7 out of the total of 150 raffle tickets sold so you have a (\( \frac{7}{150} \)) x 100 = \( \frac{7 \times 100}{150} \) = \( \frac{700}{150} \) = 5% chance to win the raffle.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 5}{6 x 5} \) - \( \frac{9 x 3}{10 x 3} \)

\( \frac{35}{30} \) - \( \frac{27}{30} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{35 - 27}{30} \) = \( \frac{8}{30} \) = \(\frac{4}{15}\)

48% of the water consumption is industrial use and 35% is personal use so (48% - 35%) = 13% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{13}{100} \) x 30,000 gallons = 3,900 gallons.

First, solve for \( \left|a - 6\right| \):

\( \left|a - 6\right| \) - 6 = 6
\( \left|a - 6\right| \) = 6 + 6
\( \left|a - 6\right| \) = 12

The value inside the absolute value brackets can be either positive or negative so (a - 6) must equal + 12 or -12 for \( \left|a - 6\right| \) to equal 12:

So, a = -6 or a = 18.