Question

1. solve the inequality and graph the solution set.

\\(50 - x - 18 + 6x \ge -38\\)

1. solve the inequality and graph the solution set.

\\(11x - 5(5x - 4) > 6\\)

1. solve the inequality and graph the solution set.

\\(-114 \ge x + 3(2x - 7) - 2\\)

1. solve the inequality and graph the solution set.

\\(5x - 3(5x + 5) - 2 < -17\\)

1. solve the inequality and graph the solution set.

\\(-2 + x - 7(4 - x) \le 2\\)

1. solve the inequality and graph the solution set.

\\(22 \le 2(3x - 6) - 13x - 1\\)

Explanation:

Solve Question 1

Using the Solving Linear Inequalities and Multi-Step Inequalities knowledge points

$$
LATEXBLOCK0
$$

Using the Graphing Inequalities knowledge point, the graph has a solid circle at \(-14\) with an arrow pointing to the right.

Solve Question 2

Using the Solving Linear Inequalities and Multi-Step Inequalities knowledge points

$$
LATEXBLOCK1
$$

Using the Graphing Inequalities knowledge point, the graph has an open circle at \(1\) with an arrow pointing to the left.

Solve Question 3

Using the Solving Linear Inequalities and Multi-Step Inequalities knowledge points

$$
LATEXBLOCK2
$$

Using the Graphing Inequalities knowledge point, the graph has a solid circle at \(-13\) with an arrow pointing to the left.

Solve Question 4

Using the Solving Linear Inequalities and Multi-Step Inequalities knowledge points

$$
LATEXBLOCK3
$$

Using the Graphing Inequalities knowledge point, the graph has an open circle at \(0\) with an arrow pointing to the right.

Solve Question 5

Using the Solving Linear Inequalities and Multi-Step Inequalities knowledge points

$$
LATEXBLOCK4
$$

Using the Graphing Inequalities knowledge point, the graph has a solid circle at \(4\) with an arrow pointing to the left.

Solve Question 6

Using the Solving Linear Inequalities and Multi-Step Inequalities knowledge points

$$
LATEXBLOCK5
$$

Using the Graphing Inequalities knowledge point, the graph has a solid circle at \(-5\) with an arrow pointing to the left.

Answer:

Question 1

• Solution: \(x \ge -14\)
• Graph: Solid circle at \(-14\), shaded to the right.

Question 2

• Solution: \(x < 1\)
• Graph: Open circle at \(1\), shaded to the left.

Question 3

• Solution: \(x \le -13\)
• Graph: Solid circle at \(-13\), shaded to the left.

Question 4

• Solution: \(x > 0\)
• Graph: Open circle at \(0\), shaded to the right.

Question 5

• Solution: \(x \le 4\)
• Graph: Solid circle at \(4\), shaded to the left.

Question 6

• Solution: \(x \le -5\)
• Graph: Solid circle at \(-5\), shaded to the left.