solve open sentence and graph the solution set

Question

1.

  ⎪2g + 5⎥  ≥ 7

 

2.

⎪m - 4⎥  ≤ -3

Answer 1

1) |2g+5| ≥ 7

Remeber the formula |x| ≥ a

Then x ≥ a or x ≤ -a

|2g+5| ≥ 7

2g+5 ≥ 7or 2g+5 ≤ -7

Now Solve 2g+5 ≥ 7

Subtract 5 from each side.

2g+5-5 ≥ 7-5

2g ≥ 2

Divide to each side by 2.

2g/2 ≥ 2/2

g ≥ 1

Now Solve 2g+5 ≤ -7

Subtract 5 from each side.

2g+5-5 ≤ -7-5

2g ≤ -12

Divide to each side by 2.

2g/2 ≤ -12/2

g ≤ -6

Solution g ≥ 1 or g ≤ -6

 

Answer 2

Graph of |2g+5| ≥ 7

The solution set is {g|g ≥ 1 or g ≤ -6}

Observe the graph the closed circle means -6 and 1 are a solutions of the absolute inequality.

2) |m-4| ≤ -3

Graph of |m-4| ≤ -3

The solution set is .

Answer 3

(1).

The absolute inequality is | 2g + 5 | ≥ 7.

| 2g + 5 | ≥ 7 is equivalent to 2g + 5 ≥ 7 or 2g + 5 ≤ -7.

Solve the inequality 1 : 2g + 5 ≥ 7 for x.

Subtract 5 from each side.

2g + 5 - 5 ≥ 7 - 5

2g ≥ 2

Divide each side by 2.

2g/2 ≥ 2/2

g ≥ 1.

 

Solve the inequality 2 : 2g + 5 ≤ -7 for x.

Subtract 5 from each side.

2g + 5 - 5 ≤ - 7 - 5

2g ≤ - 12

Divide each side by 2.

2g/2 ≤ - 12/2

g ≤ - 6.

 

The solution set is {g | g ≥ 1 or g ≤ -6} and its graph is

Note : A dot means that this point is included in the solution set.

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(2).

The absolute inequality is | m - 4 | ≤ - 3.

Since | m - 4 | cannot be negative, | m - 4 | cannot be less than or equal to -1. So, the solution set is the empty set ø and its graph is