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mixer [17]
3 years ago
9

1. Let a be a positive real number. In Part (1) of Theorem 3.25, we proved that for each real number x, jxj < a if and only i

f a < x < a. It is important to realize that the sentence a < x < a is actually the conjunction of two inequalities. That is, a < x < a means that a < x and x < a. ? (a) Complete the following statement: For each real number x, jxj a if and only if . . . . (b) Prove that for each real number x, jxj a if and only if a x a. (c) Complete the following statement: For each real number x, jxj > a if and only if .
Mathematics
1 answer:
krek1111 [17]3 years ago
8 0

Answer:

(a)

if x \geq 0 then  x \geq a and if x<0 then -x > a

(b)

That is straightforward from what you showed on theorem 3.25

(c)

Following the same ideas from (a) x>a or -x > a.

Step-by-step explanation:

Remember how we define the absolute value of a number.

(a)

In general

|x| = x  \,\,\,\text{if}  \,\,\,\, x \geq 0 \\|x| = -x  \,\,\,\text{if}  \,\,\,\, x < 0

Therefore if |x| \geq a   you have two cases, if x \geq 0 then  x \geq a and if x<0 then -x > a

(b)

That is straightforward from what you showed on theorem 3.25

(c)

Following the same ideas from (a) x>a or -x > a.

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What is the solution to -(4x-3) = -7(9+x) ???
Likurg_2 [28]

Answer:

The solution is -22

Step-by-step explanation:

<em>The solution of an equation is the value of the variable of the equation</em>

∵ -(4x - 3) = -7(9 + x)

→ Simplify each side

∵ -(4x) - -(3) = -7(9) + -7(x)

∴ (-4x) - (-3) = -63 + (-7x)

→ Remember (-)(-) = (+) and (-)(+) = (-)

∴ -4x + 3 = -63 - 7x

→ Add 7x to both sides

∴ -4x + 7x + 3 = -63 - 7x + 7x

∴ 3x + 3 = -63

→ Subtract 3 from both sides

∵ 3x + 3 - 3 = -63 - 3

∴ 3x = -66

→ Divide both sides by 3

∴ x = -22

∴ The solution is -22

8 0
3 years ago
Philip walked a total of 8 kilometers by making 2 trips to school. After 3 trips to school, how many kilometers will Philip have
vekshin1
So one trip = 4 km
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Thanks!
7 0
3 years ago
Read 2 more answers
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Gnesinka [82]

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Step-by-step explanation:

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6 0
3 years ago
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3 years ago
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8 0
2 years ago
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