Solve each compound inequality and graph the solution:
2(4x + 3) ≥ -10 or -5x - 15 > 5

Solve each compound inequality and graph the solution
-x+1 > -2 and 6(2x-3) ≥ -6

Solve each compound inequality and graph the solution:
4x - 1 > 3 and -2(3x - 4) ≥ -16

Inequalities define the relationship between two values that are not equal. Not equal is the definition of inequality. In most cases, we use the "not equal symbol (≠)" to indicate that two values are not equal. But several inequalities are employed to compare the values, whether they are less than or more.
Step 1: The values on the number line that satisfy each inequality in the compound inequality are shaded on the graph. The graph's endpoint should be marked with a filled-in circle to show that a value included in the inequality symbol is either or; otherwise, the endpoint should be marked with an open circle to show that a value is not included. There should be an arrow pointing in that direction at the end of the graph that never ends.
Step 2: The graph of the compound inequality is the intersection of the two graphs from Step 1 if the compound inequality contains the term AND. Only the portion of the number line that appears in both graphs should be shaded. The graph of the compound inequality is the union of the two graphs from Step 1 if the compound inequality contains the term OR. Incorporate both of these graphs into the last one.

Find the distance between the lines y = x + 1 and y = x – 1

Solve each compound inequality and graph the solution

What is the least number of blocks Alex has to travel to reach Kevin?

 

Write a compound inequality for each graph:

What is the shortest path between points A and B?

Draw the taxicab circle with the given radius r and centre C.
I) r = 1, C = (1, 1)
II) r = 2, C = (-2, -2)

Solve each compound inequality and graph the solution

On the number line, we can graph the compound inequalities. When graphing compound inequalities, keep the following points in mind.
• Consider a number on the number line that corresponds to the inequality. For example, if x > 2, we must determine where '2' falls on the number line.
• If the inequality is either ">" or "<, "place an open dot (to indicate that the value is "NOT" included).
If the inequality is either "≥" or " ≤, "place a closed dot to include the value.
For example, if x > 2, place an open dot at '2' because the inequality is strict and does not include " =."
• Place an arrow symbol on the right side of the number for the ">" or "≥" sign.
• Place an arrow symbol on the left side of the number for the " <"or " ≤" sign.
• Finally, use the intersection or union, depending on whether "AND" or "OR" is given, to find the final solution.

The sum of two expressions is x³ -x² + 3x- 2. If one of them is x² + 5x- 6, what is the
other?

Find the missing coordinate k if the taxicab distance between (-7, 10) and (k, 5) is 8.

Write the compound inequality for the graph :

Find the taxicab distance between (-5, 7) and (0, 4).

The length of a rod is 4x + 5y- 3z cm and the length of another is 6x- 3y + z cm. By
How much is the second rod longer than the first?

Kona Graphed the compound inequality x > 2 or x > 3 by graphing x > 3. Explain Kona’s error.

We will use the following steps to solve a system of linear inequalities graphically as per Kona's error described in the question:
1. Determine the inequality for y.
2. Graph the line as a solid or dashed line depending on the sign of the inequality.
• Draw the line as a dashed line if the inequality sign lacks an equals sign (or >).
• If the inequality sign includes an equals sign, draw the line as a solid line (or).
3. Highlight the area that satisfies the inequality.
4. Repeat steps 1–3 for each inequality.
5. The overlapping region of all the inequalities will be the solution set.