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podryga [215]
3 years ago
6

Which graph shows the solution to the system of linear inequalities?

Mathematics
1 answer:
Dima020 [189]3 years ago
5 0

Answer:

We can not see all the graphs, so i will just do a graph of the system of inequalities, and you can select the option that matches it.

We have the system:

y ≥ 2x + 1

(to represent this, we need to have a solid line y = 2x + 1, and shade all the region above this)

y ≤ 2x - 2

(to represent this, we need to have a solid line y = 2x - 2, and shade all the region below this)

The graph of this system is shown below:

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1/3(z+4)-6=2/3(5-z) solve for z and check solution
Marat540 [252]

Answer:

z = 8

Step-by-step explanation:

Solve for z:

(z + 4)/3 - 6 = (2 (5 - z))/3

Put each term in (z + 4)/3 - 6 over the common denominator 3: (z + 4)/3 - 6 = (z + 4)/3 - 18/3:

(z + 4)/3 - 18/3 = (2 (5 - z))/3

(z + 4)/3 - 18/3 = ((z + 4) - 18)/3:

(z - 18 + 4)/3 = (2 (5 - z))/3

Add like terms. 4 - 18 = -14:

(z - 14)/3 = (2 (5 - z))/3

Multiply both sides by 3:

(3 (z - 14))/3 = (3×2 (5 - z))/3

(3 (z - 14))/3 = 3/3×(z - 14) = z - 14:

z - 14 = (3×2 (5 - z))/3

(3×2 (5 - z))/3 = 3/3×2 (5 - z) = 2 (5 - z):

z - 14 = 2 (5 - z)

Expand out terms of the right hand side:

z - 14 = 10 - 2 z

Add 2 z to both sides:

2 z + z - 14 = (2 z - 2 z) + 10

2 z - 2 z = 0:

2 z + z - 14 = 10

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3 z - 14 = 10

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3 z + (14 - 14) = 14 + 10

14 - 14 = 0:

3 z = 10 + 14

10 + 14 = 24:

3 z = 24

Divide both sides of 3 z = 24 by 3:

(3 z)/3 = 24/3

3/3 = 1:

z = 24/3

The gcd of 24 and 3 is 3, so 24/3 = (3×8)/(3×1) = 3/3×8 = 8:

Answer:  z = 8

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