Question
The compound inequality x > a and x > b is graphed below. How is the point labelled c related to a and b?
Hint:
If two real numbers or algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality. For example, x>5 (x should be greater than 5).
A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. “Or” indicates that, as long as either statement is true, the entire compound sentence is true.
If the symbol is (≥ or ≤) then you fill in the dot and if the symbol is (> or <) then you do not fill in the dot.
The correct answer is: if a > b then a = c, if b > a then b = c and if a = b then a = b = c.
Let’s say that a > b
So if a > b
Then a = c
If b > a
Then b = c
If a = b
Then a = b = c
Final Answer:
Hence, if a > b then a = c, if b > a then b = c and if a = b then a = b = c.
Then a = c
If b > a
Then b = c
If a = b
Then a = b = c
Final Answer:
Hence, if a > b then a = c, if b > a then b = c and if a = b then a = b = c.
When working with inequalities, we can treat them similarly to, but not identically to, equations. We can use the addition and multiplication properties to help us solve them. The inequality symbol must be reversed when dividing or multiplying by a negative number. This question concluded that inequalities have the following properties:
A GENERAL NOTE: PROPERTIES OF INEQUALITIES
Addition Property: If a<b, then a + c < b + c.
Multiplication Property: If a < b and c > 0, then ac < b c and a<b and c < 0, then ac > bc.
These properties also apply to a ≤ b, a > b, and a ≥ b.
Related Questions to study
Solve each compound inequality and graph the solution
2x-5 > 3 and -4x+7 < -25
Divide a compound inequality into two individual inequalities before solving it. The solution should either be a union of sets ("or") or an intersection of sets ("and"). After that, resolve the graph and all inequalities.
Use the steps below to resolve an inequality:
Step 1: Fractions are first eliminated by multiplying all terms by the total fractions' lowest common denominator.
Step 2: Simplify the inequality by combining like terms on each side.
Step 3: Subtract or add quantities to get the unknown on one side and the numbers on the other.
Solve each compound inequality and graph the solution
2x-5 > 3 and -4x+7 < -25
Divide a compound inequality into two individual inequalities before solving it. The solution should either be a union of sets ("or") or an intersection of sets ("and"). After that, resolve the graph and all inequalities.
Use the steps below to resolve an inequality:
Step 1: Fractions are first eliminated by multiplying all terms by the total fractions' lowest common denominator.
Step 2: Simplify the inequality by combining like terms on each side.
Step 3: Subtract or add quantities to get the unknown on one side and the numbers on the other.
The slope of line a is – 4. Line b is perpendicular to line a. The equation of line c is 3y + 12x = 6. What is the relation between line b and line c?
The slope of line a is – 4. Line b is perpendicular to line a. The equation of line c is 3y + 12x = 6. What is the relation between line b and line c?
Nadeem plans to ride her bike between 12 mi and 15 mi. Write and solve an inequality to model how many hours Nadeem will be riding?
In this question, the time taken to ride by Nadeem is to be calculated with the help of the speed and distance formula (time = distance/speed). So, for example, to determine the time required to complete a journey, we must first know the distance and speed.
There are three different ways to write the formula. They are:
• speed = distance ÷ time
• distance = speed × time
• time = distance ÷ speed
Calculating with the time formula gives us the answer as an inequality.
Nadeem plans to ride her bike between 12 mi and 15 mi. Write and solve an inequality to model how many hours Nadeem will be riding?
In this question, the time taken to ride by Nadeem is to be calculated with the help of the speed and distance formula (time = distance/speed). So, for example, to determine the time required to complete a journey, we must first know the distance and speed.
There are three different ways to write the formula. They are:
• speed = distance ÷ time
• distance = speed × time
• time = distance ÷ speed
Calculating with the time formula gives us the answer as an inequality.
Solve each compound inequality and graph the solution:
2(4x + 3) ≥ -10 or -5x - 15 > 5
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
-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.
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
Find the distance between the lines y = x + 1 and y = x – 1
Solve each compound inequality and graph the solution
Solve each compound inequality and graph the solution
What is the least number of blocks Alex has to travel to reach Kevin?
What is the least number of blocks Alex has to travel to reach Kevin?
Write a compound inequality for each graph:
Write a compound inequality for each graph:
What is the shortest path between points A and B?
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)
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.
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.
