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2 years ago

Solve |x–1| = 6x + 12

Mathematics

1 answer:

frutty [35]2 years ago

3 0

Answer:

$x = - \frac{11}{7}$

Step-by-step explanation:

1) Break down the problem into these 2 equations.

$x - 1 = 6x + 12$

$- (x - 1) = 6x + 12$

2) Solve the first equation. x - 1 = 6x + 12

$x = - \frac{13}{5}$

3) Solve the second equation: -( x - 1 ) = 6x + 12.

$x = - \frac{11}{7}$

4) Collect all solution.

$x = - \frac{13}{5}. - \frac{11}{7}$

5) Check solution.

When x=-\frac{13}{5}x=−513, the original equation |x-1|=6x+12∣x−1∣=6x+12 does not hold true.

When x=-\frac{13}{5}x=−513, the original equation |x-1|=6x+12∣x−1∣=6x+12 does not hold true.We will drop x=-\frac{13}{5}x=−513 from the solution set.

6) Simplify.

$x = - \frac{11}{7}$

Therefor, the answer is x = - 11/7.

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a) The distribution of cracked eggs per dozen should be a binomial distribution B(12,0.01), as it can model 12 independent events.

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$P(k=0)=\binom{1200}{0}p^0(1-p)^{12}=1*1*0.99^{1200}=1* 0.000006 = 0.000006 \\\\ P(k=1)=\binom{1200}{1}p^1(1-p)^{1199}=1200*0.01*0.99^{1199}=1200*0.01* 0.000006 \\\\P(k=1)= 0.00007\\\\\\P(k\leq1)=0.000006+0.000070=0.000076\\\\\\P(k>1)=1-P(k\leq 1)=1-0.000076=0.999924$