I am trying to pass algebra have so much work please help me thank you so much it is just two questions?

Question

1.) Solve -2x + 1 less than or greater to -7 and describe the graph of the solution.

2.) A solution to the compound inequality 8 > 5 - 3x > -13 is provided below. Choose the statement that is true about the given solution.

Answer 1

2) The compound inequality is 8 > 5 - 3x > -13

Subtract 5 from each side

8-5 > 5 - 3x-5 > -13-5

3 > - 3x > -18

Divide each side by negative 3 and flip the symbol

3/-3 < - 3x/-3 < -18/-3

-1 < x < 6

The compound inequality solution set is {x / -1 < x < 6}

Comments

The solution set of the compound inequality is {x |-1 < x < 6} or (-1, 6) or [0, 1, 2, 3, 4, 5].

since the compound inequality contain the less than symbol, the numbers -1 and 6 are not solutions.

CHECK :

The

Test Interval    x-value                 compound inequality                      conclusion

(-∞, -1)          x = - 2           8 > 5 - 3(-2) > -13  ⇒ 8 > 11 > -13           false

(1, 6)              x = 0             8 > 5 - 3(0) > -13  ⇒ 8 > 5 > -13              true

(1, 6)              x = 1             8 > 5 - 3(1) > -13  ⇒ 8 > 2 > -13              true

(1, 6)              x = 2             8 > 5 - 3(2) > -13  ⇒ 8 > - 1 > -13            true

(1, 6)              x = 3             8 > 5 - 3(3) > -13  ⇒ 8 > - 4 > -13            true

(1, 6)              x = 4             8 > 5 - 3(4) > -13  ⇒ 8 > - 7 > -13            true

(1, 6)              x = 5             8 > 5 - 3(5) > -13  ⇒ 8 > - 10 > -13          true

(6, ∞)             x = 7             8 > 5 - 3(7) > -13  ⇒ 8 > - 16 > -13          false

From the table, we conclude that the statement is true for (1, 6).

Answer 2

(1).

The compound inequality is -2x+1 < -7 or -2x + 1> -7.

Solve the inequality  1 :  -2x+1 < -7 for x.

subtract 1 from each side.

-2x+1 - 1 < -7 - 1

-2x < -8

Divide each side by negative 2 and the reverse the inequality symbol.

(-2x)/(-2) > (-8)/(-2)

x > 4.

 

Solve the inequality 2 :  -2x + 1> -7 for x.

subtract 1 from each side.

-2x + 1- 1 > -7 - 1

-2x > -8

Divide each side by negative 2 and the reverse the inequality symbol.

(-2x)/(-2) < (-8)/(-2)

x < 4.

 

Therefore, solution of the compound inequality is all real numbers except 4.

The graph of the solution set {x | x ∈ R, x ≠ 4} is