Indicate the region of the number line that represents the following: B) x

Question

Indicate the region of the number line that represents the following: B) x <= −2 OR x < −4; C) x <= 2 OR x >= 6

ScanSolve AI Tutor · Accepted Answer

here are the number line representations for the remaining parts of Question 2:

Indicate the region of the number line that represents the following.

B) $x \le -2$ OR $x < -4$

Understand the first inequality, $x \le -2$ .
This means $x$ is less than or equal to -2. On a number line, this is represented by a solid dot at -2 and shading to the left.
Understand the second inequality, $x < -4$ .
This means $x$ is less than -4. On a number line, this is represented by an open dot at -4 and shading to the left.
Combine the inequalities using "OR".
The "OR" condition means that $x$ must satisfy at least one of the inequalities. Since all numbers less than or equal to -2 also include numbers less than -4, the combined region is $x \le -2$ .

Number line representation:
Draw a number line. Place a solid dot (•) at -2. Shade the region to the left of -2.
$\text{<---•--------------------->}$ $\quad \quad \text{-2}$
C) $x \le 2$ OR $x \ge 6$
Understand the first inequality, $x \le 2$ .
This means $x$ is less than or equal to 2. On a number line, this is represented by a solid dot at 2 and shading to the left.
Understand the second inequality, $x \ge 6$ .
This means $x$ is greater than or equal to 6. On a number line, this is represented by a solid dot at 6 and shading to the right.
Combine the inequalities using "OR".
The "OR" condition means that $x$ must satisfy at least one of the inequalities. These are two separate regions.

Number line representation:
Draw a number line. Place a solid dot (•) at 2 and shade to the left. Place a solid dot (•) at 6 and shade to the right.
$\text{<---•--------------------•--->}$ $\quad \quad \text{2} \quad \quad \quad \quad \quad \text{6}$
D) $x < -2$ AND $x \ge -7$
Understand the first inequality, $x < -2$ .
This means $x$ is less than -2. On a number line, this is represented by an open dot at -2 and shading to the left.
Understand the second inequality, $x \ge -7$ .
This means $x$ is greater than or equal to -7. On a number line, this is represented by a solid dot at -7 and shading to the right.
Combine the inequalities using "AND".
The "AND" condition means that $x$ must satisfy both inequalities simultaneously. The region where both are true is between -7 (inclusive) and -2 (exclusive).

Number line representation:
Draw a number line. Place a solid dot (•) at -7. Place an open dot (○) at -2. Shade the region between -7 and -2.
$\text{<---•------------------○--->}$ $\quad \quad \text{-7} \quad \quad \quad \quad \quad \text{-2}$
E) $x \ge 0$ OR $x \le -6$
Understand the first inequality, $x \ge 0$ .
This means $x$ is greater than or equal to 0. On a number line, this is represented by a solid dot at 0 and shading to the right.
Understand the second inequality, $x \le -6$ .
This means $x$ is less than or equal to -6. On a number line, this is represented by a solid dot at -6 and shading to the left.
Combine the inequalities using "OR".
The "OR" condition means that $x$ must satisfy at least one of the inequalities. These are two separate regions.

Number line representation:
Draw a number line. Place a solid dot (•) at -6 and shade to the left. Place a solid dot (•) at 0 and shade to the right.
$\text{<---•--------------------•--->}$ $\quad \quad \text{-6} \quad \quad \quad \quad \quad \text{0}$

Indicate the region of the number line that represents the following: B) x <= -2 OR x < -4; C) x <= 2 OR x >= 6

Step-by-step solution

Understand the first inequality, $x \le -2$ .

Understand the second inequality, $x < -4$ .

Combine the inequalities using "OR".

Understand the first inequality, $x \le 2$ .

Understand the second inequality, $x \ge 6$ .

Combine the inequalities using "OR".

Understand the first inequality, $x < -2$ .

Understand the second inequality, $x \ge -7$ .

Combine the inequalities using "AND".

Understand the first inequality, $x \ge 0$ .

Understand the second inequality, $x \le -6$ .

Combine the inequalities using "OR".

Still stuck on this one?

More Mathematics Questions

Indicate the region of the number line that represents the following: B) x <= -2 OR x < -4; C) x <= 2 OR x >= 6

Step-by-step solution

Understand the first inequality, x≤−2x \le -2x≤−2.

Understand the second inequality, x<−4x < -4x<−4.

Combine the inequalities using "OR".

Understand the first inequality, x≤2x \le 2x≤2.

Understand the second inequality, x≥6x \ge 6x≥6.

Combine the inequalities using "OR".

Understand the first inequality, x<−2x < -2x<−2.

Understand the second inequality, x≥−7x \ge -7x≥−7.

Combine the inequalities using "AND".

Understand the first inequality, x≥0x \ge 0x≥0.

Understand the second inequality, x≤−6x \le -6x≤−6.

Combine the inequalities using "OR".

Still stuck on this one?

More Mathematics Questions

Understand the first inequality, $x \le -2$ .

Understand the second inequality, $x < -4$ .

Understand the first inequality, $x \le 2$ .

Understand the second inequality, $x \ge 6$ .

Understand the first inequality, $x < -2$ .

Understand the second inequality, $x \ge -7$ .

Understand the first inequality, $x \ge 0$ .

Understand the second inequality, $x \le -6$ .