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sdas [7]
3 years ago
13

Solve the compound inequality |3x-9|≤15 and |2x-3|≥5. Give answer in interval notation.

Mathematics
1 answer:
laila [671]3 years ago
6 0

Answer:

The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is  (-∞,2] ∪ [8,∞)

Step-by-step explanation:

When solving absolute value inequalities, there are two cases to consider.

Case 1: The expression within the absolute value symbols is positive.

Case 2: The expression within the absolute value symbols is negative.

The solution is the intersection of the solutions of these two cases.

In other words, for any real numbers a and b,

  • if |a|> b then a>b or a<-b
  • if |a|< b then a<b or a>-b

So, being |3x-9|≤15

Solving: 3x-9 ≤ 15

3x ≤15 + 9

3x ≤24

x ≤24÷3

x≤8

or 3x-9 ≥ -15

3x ≥-15 +9

3x ≥-6

x ≥ (-6)÷3

x ≥ -2

The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]

So, being |2x-3|≥5

Solving: 2x-3 ≥ 5

2x ≥ 5 + 3

2x ≥8

x ≥8÷2

x≥8

or 2x-3 ≤ -5

2x ≤-5 +3

2x ≤-2

x ≤ (-2)÷2

x ≤ -2

Expressing the solution as an interval: (-∞,2] ∪ [8,∞)

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Write an equation in point-slope form of the line that passes through the given point and has the given slope. (3, –8); m = –5
Paraphin [41]

Answer:

y+8=-5(x-3)

Step-by-step explanation:

The formula for point-slope form is y-y1=m(x-x1)

The points for (x1, y1) are (3, -8), meaning that 3 is x1 and -8 is y1.

So, start by writing your equation like this: y--8=m(x-3)

For the equation y--8=m(x-3), the y--8 will change to a + sign because two negatives make a positive, right? So, the equation should now look like this: y+8=m(x-3).

We know that the slope (m) is -5. Plug that into the equation to get this: y+8=-5(x-3)

And there you have it!! The equation is now in point-slope form!!

y+8=-5(x-3) is the final answer!!

Hope that helps you!! Please give me brainliest!!

7 0
3 years ago
Is 1/2 greater than 2/5
Free_Kalibri [48]
yes it is greater than 2/5


6 0
3 years ago
PLEASE HELP AGAIN ASAP!
Dovator [93]
15/5 goes to all of them..

15/5 = 3
8 0
3 years ago
Aaron borrows $150 from his friend Austin. He promises to pay back the money in 4 monthly installments. Each month he wants to p
dalvyx [7]
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6 0
3 years ago
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Ahoy there, matey! Our pirate ship had 5/6 of a treasure chest full of gold.
Kisachek [45]

Answer:

1 \frac{5}{24} teasure chests of gold

Step-by-step explanation:

Since this is a problem of adding or subtracting fractions, you will have to do one or the other to solve.  Since the pirates already had \frac{5}{6} of a treasure chest of gold and stole another \frac{3}{8} of a treasure chest to add to their collection, we need to add these two fractions:

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6: 6, 12, 18, 24

8: 8, 16, 24

\frac{5}{6}=\frac{20}{24}and\frac{3}{8}=\frac{9}{24}

Add them together:  \frac{20}{24}+\frac{9}{24}=\frac{29}{24}=1\frac{5}{24}

7 0
3 years ago
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