Question
Let a, b and c be real numbers, c≠0, Show that each of the following statements is true :
1. If a>b and c<0 , then ca< cb
2. If a>b and c<0 , then .
Hint:
Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .
We are asked to prove the given statements.
The correct answer is: a/c<b/c
Step 1 of 2:
Given that, a<b and c<0.
Multiply c with the inequality, so we get:
Here, the direction of symbol changes because we multiplied the inequality by a negative number.
Step 2 of 2:
Similar to the previous step, here we divide the inequality by a negative number and hence the direction of the symbol changes.
Whenever we multiply or divide an inequality by a negative number, the direction of the inequality symbol changes.
Related Questions to study
The graph above shows the distance traveled d, in feet, by a product on a conveyor belt m minutes after the product is placed on the belt. Which of the following equations correctly relates d and m?
The graph above shows the distance traveled d, in feet, by a product on a conveyor belt m minutes after the product is placed on the belt. Which of the following equations correctly relates d and m?
3x + x + x + x - 3 – 2 = 7+ x + x
In the equation above, what is the value of x?
3x + x + x + x - 3 – 2 = 7+ x + x
In the equation above, what is the value of x?
A certain sum at simple interest amounts to Rs. 3,900 in 3 years and Rs. 4,500 in 5 years. Find the sum and rate of interest per annum.
A certain sum at simple interest amounts to Rs. 3,900 in 3 years and Rs. 4,500 in 5 years. Find the sum and rate of interest per annum.
A square has vertices (0, 0), (1, 0), and (0, 1). Find the fourth
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A square has vertices (0, 0), (1, 0), and (0, 1). Find the fourth
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Lourdes plans to jog at least 1.5 miles . Write and solve an inequality to find X, the number of hours Lourdes will have to jog.
A distance is generally the amount of space or length that separates two people, objects, or situations. For example, four meters separate two streetlight poles, for instance, as a distance measure.
Where Distance = time × speed
Example: We kept a safe distance between two objects. At the same time, we notice a new space between object one and object 2. Although once close, there was a significant gap between the objects. However, wishes to distance themself from the object's former boss.
Lourdes plans to jog at least 1.5 miles . Write and solve an inequality to find X, the number of hours Lourdes will have to jog.
A distance is generally the amount of space or length that separates two people, objects, or situations. For example, four meters separate two streetlight poles, for instance, as a distance measure.
Where Distance = time × speed
Example: We kept a safe distance between two objects. At the same time, we notice a new space between object one and object 2. Although once close, there was a significant gap between the objects. However, wishes to distance themself from the object's former boss.
A square has vertices (0, 0), (m, 0), and (0, m). Find the fourth
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A square has vertices (0, 0), (m, 0), and (0, m). Find the fourth
vertex.
Solve inequality : 3x-2>4-3x and then graph the solution.
Note:
When we have an inequality with the symbols< or > , we use dotted lines to graph them. This is because we do not include the end point of the inequality.
Solve inequality : 3x-2>4-3x and then graph the solution.
Note:
When we have an inequality with the symbols< or > , we use dotted lines to graph them. This is because we do not include the end point of the inequality.
and then graph the solution.
