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

vertex.

### A square has vertices (0, 0), (1, 0), and (0, 1). Find the fourth

vertex.

### 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

vertex.

### 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.