−2∣5w−7∣+9=−7 What is the 2 answers for this question

1 answer:

5 0

The two possible answers are w = 3 and w = -1/5

These answers can be obtained through solving to the absolute value symbols.

−2∣5w−7∣+9=−7 ---> subtract 9 from both sides
−2∣5w−7∣= -16 ---> divide both sides by -2
∣5w−7∣= 8

Now, because of the absolute value symbols, set the inside equal to 8 and -8 for the two answers.

5w - 7 = 8
5w = 15
w = 3

AND

5w - 7 = -8
5w = -1
w = -1/5

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What are the solutions of |x+6| greater than or equal to 5? Write the solutions as either the union or the intersection of two s

sukhopar [10]

We have that
 |x+6| >= 5
step 1
resolve for (x+6)>=5------> x>=5-6-------> x>= -1
the solution is the interval (-1, ∞)

step 2
resolve for -(x+6) >=5------> -x-6 >=5----> -x >= 5+6---> -x>=11----> x<=-11
the solution is the interval (-∞, -11)

using a graph tool
see the attached figure

the solution is the interval (-∞, -11) ∩ (-1, ∞)