Question

# What is the solution of 0.2 x -4 - 2x < - 0.4 and 3x + 2.7 <3 ?

- x = 0.1
- x < 0.2
- - 2 < x < 0.1
- x < - 2 and x > 0.1

Hint:

### This is a question of compound inequalities. A compound inequality means we are given two statements. It is joined using the words “and” and “or”. We have to find the values of the variables satisfying those statements. We will simply the equations using the rules to solve inequalities.

## The correct answer is: - 2 < x < 0.1

### The given inequalities are as follows:

0.2x – 4 – 2x < -0.4 and 3x + 2.7 < 3

The word used to join them is “and”. So, we have to find the values of x satisfying both the statements.

When the word “and” is used, the values of the variables simultaneously satisfy both the inequalities.

When the word “or” is used, the values of the variables satisfy either of the inequalities.

We will solve the inequalities one by one.

0.2x – 4 – 2x < -0.4

We will take the variables together and solve them first.

0.2x – 2x – 4 < - 0.4

- 1.8x – 4 < - 0.4

We will isolate the variable by adding 4 to both the sides.

-1.8x – 4 + 4 < -0.4 + 4

- 1.8x < 3.6

Now, we will divide both the sides by -1.8. As we are dividing by a negative number, the inequality will flip.

x > -2

3x + 2.7 < 3

We will isolate the variable by subtracting 2.7 from both the sides.

3x + 2.7 – 2.7 < 3 – 2.7

3x < 0.3

Dividing both the sides by 3 we get,

x < 0.1

Now, the values satisfying the two inequalities are given as follows:

x > -2

x < 0.1

We can combine the solution and write the intersection of the solution as follow:

-2 < x < 0.1

So, the solution is -2 < x < 0.1.

We have to follow the rules of inequalities to solve such questions. We have to swap the inequality when we divide it or multiply it by a negative number. In such questions, we find the values of the variables which makes the statement of inequalities true.

### Related Questions to study

### Find the area of the right-angled triangle if the height is 5 units and the base is *x* units, given that the area of the triangle lies between 10 and 35 sq. units

An **inequality** is a relation which makes a non-equal comparison between two numbers or other mathematical expressions

### Find the area of the right-angled triangle if the height is 5 units and the base is *x* units, given that the area of the triangle lies between 10 and 35 sq. units

An **inequality** is a relation which makes a non-equal comparison between two numbers or other mathematical expressions

### Solve - 8 < 2 (x + 4) or - 3x + 4 > x - 4

Inequality reverse if we multiply both side with -1

### Solve - 8 < 2 (x + 4) or - 3x + 4 > x - 4

Inequality reverse if we multiply both side with -1

### Write the compound inequality that represents the area A of the rectangle if 35 ≥ A ≥ 25.

### Write the compound inequality that represents the area A of the rectangle if 35 ≥ A ≥ 25.

### The inequality that is represented by graph 4 is ______.

### The inequality that is represented by graph 4 is ______.

### The compound function that represents the graph is __________.

### The compound function that represents the graph is __________.

### Write a compound inequality for the given graph

### Write a compound inequality for the given graph

### Which inequality is the same as “pick a number between -3 and 7?”

### Which inequality is the same as “pick a number between -3 and 7?”

### Solve 12 < 2x < 28

Inequality reversed, if we multiply both side by -1

### Solve 12 < 2x < 28

Inequality reversed, if we multiply both side by -1

### A compound inequality including “and” has the solutions of ___________.

### A compound inequality including “and” has the solutions of ___________.

### The two inequalities form a ______________.

### The two inequalities form a ______________.

### Solve the inequality:

0.6x ≤ 3

Inequality reversed, if we multiply both side by -1

### Solve the inequality:

0.6x ≤ 3

Inequality reversed, if we multiply both side by -1