An Occasion as one of the Activities for Preparing Lesson Plan (RPP) for Teaching Learning Linear Inequality With One Variable for SMP Students Grade 7

By: Marsigit

Basic Competence

• To solve linear inequality with one variable

• To construct the mathematical models for the problems related to linear equation and inequality with one variable.

• To solve the mathematical models for the problems related to linear equation and inequality with one variable.

Illustration:

Truck is a vehicle used to carry heavy and large amount of goods. There are many kind of trucks; it depends on the maximum weight of goods will be carried. In general there are three kinds of trucks such as follows:

• Light weight truck. It carries less than 6.300 kg of goods.

• Middle weight truck. It carries between 6.300 kg and 15.000 kg of goods.

• Heavy weight truck. It carries more than 15.000 kg of goods.

The words : less than, between, and more than are frequently used in linear inequality with one variable.

What will you learn in this Lesson?

• To understand the linear inequality with one variable.

• To solve linear inequality with one variable.

• To apply linear inequality with one variable.

A. Understanding the Linear Inequality with One Variable

1. The Concept of Inequality

• Equality is a state of being equal representing by the sentences connected by the sign “ = “ on both sides.

Example : 5 + 3 = 8

• Equation is a statement of equality between two expressions involving one or more unknown quantities, called variables. The expressions are connected by the sign “ = “

Example : x + 3 = 8

• Inequality is a statement indicating that two quantities are not equal, represented by the symbol <, >, or ≠, meaning less than, greater than, and not equal to.

Example : 5 + 4 ≠ 3

6 + 8 ≥ 7

• Inequality with variable is a statement involving variables indicating that two quantities are not equal, represented by the symbol <, >, or ≠, meaning less than, greater than, and not equal to.

Example : x + 6 ≠ 2

y – 4 > -5

Note :

A statement is a true or false mathematical sentence

Open sentence is a mathematical sentence in which its truth value has not been determined yet.

Example

Determine if the following sentences is an inequality or inequality with variable

1).12 – 3 ≤ 10 2). x + 6 > 3x - 2 3). 7 + 7 ≠ 30 : 2

Solution:

1. The sentence of 12 – 3 ≤ 10 is an inequality

2. The sentence of x + 6 > 3x – 2 is an inequality with variable

3. The sentence of 7 + 7 ≠ 30 : 2 is an inequality

Exercise

Determine if the following sentences is an inequality or inequality with variable

1. x + y ≥ 4

2. 92 ≠ 9 + 9

3. 10 ≤ 100 – 2 + y

4. 2x – 12 ≠ 3

5.6 + 2x < style="font-weight: bold;">2. The Concept of Linear Inequality with One Variable

An inequality that contains one variable of which the power is one is called a linear inequality with one variable.

Example

Write down the following sentences into a linear inequality with one variable.

1. The speed of a car cannot be more than 60 km/hr and cannot be less than 40 km/hr.

2. An air balloon can be ridden by four to six passengers.

Solution:

1. Let the speed of a car is v. You can express “the speed of a car cannot be more than 60 km/hr” as v ≤ 60. “The speed of a car cannot be less than 40 km/hr” can be expressed as v ≥ 40, or 40 ≤ v. Therefore, “The speed of a car cannot be more than 60 km/hr and cannot be less than 40 km/hr” can be written as v ≤ 60 and 40 ≤ v. Thus, it can be simplified as 40 ≤ v ≤ 60.

2. Let, the number of passengers is x, you can write that “An air balloon can be ridden by four to six passengers” as 4 ≤ x ≤ 6.

Exercise

Write down the following sentences into a linear inequality with one variable.

1. Twice of Tanti’s age is less than 32 years.

2. Father’s weight is between 55 to 60 kg.

3. Twice of a number is more than the number decreased by 21.

4. The candidate must be 25 to 30 years old.

5. Five times a number decreased by 11 is more than three times the number decreased by 6.

B. Solving Linear Inequality with One Variable

1. The Concept of Rational Numbers

Rational numbers are the extension of integers and fractions. Therefore rational numbers consist of integers and all fractions.

Rational number is a number that can be written in the form of , where a and b are integers and b ≠ 0.

Example

Determine whether the following numbers is rational number?

1. 3 2. 3.

Solution

1. Three is rational number, because it can be written as , that is .

2. Minus a half is rational number because it is equal to the definition of rational number.

3. is not rational number because it can’t be written as , where a and b are integers and b ≠ 0.

Note :

Try to calculate by your calculator, you’ll find 1,4142 as the result.

Exercise

Which one of the following numbers is rational number?

1. 0 2. 3. 4. 5.

If you want to sketch x > -3, where x is an integer, into line number, you’ll find the following graph.

But, if you want to sketch x > -3, where x is a rational number, you’ll find the following graph.

Why the graphs are so different? The second line tell us that the solutions of x > -3 are not only integers, as -2 or -1, but also fractions as or .

2. The Solutions of Linear Inequality with One Variable

Consider the inequality of t + 2 > 6. To find the solutions of the inequality, first, you pay attention to equation of t + 2 = 6. Then solve it.

The value of t = 4 is called zero value of the inequality of . Try to substitute t by the numbers which is more than 4 or less than 4., i.e. 5 and 3.

• For t = 5, the inequality of will be a true statement, that is .

• For t = 3, the inequality of will be a wrong statement, that is .

Therefore, the solution set of where t are rational numbers, is t > 4.

Example

Find the solution of , where y are natural numbers. Then, sketch the graph of the solution.

Solution

First, find the zero value of the inequality of by changing it into the form of .

both sides are added by 11

both sides are divided by 4

Check for y > 5 and y < y =" 6" y =" 4." y =" 6," y =" 4," y =" 4," y =" 3," y =" 2," y =" 1." style="font-weight: bold;">Exercise

Find the solutions of the following inequalities. Make its line-numbers.

1. , where x are rational numbers.

2. , where x are integers.

3. , where x are whole numbers.

4. , where x are natural numbers less than 15.

5. , where x are rational numbers.

3. The Equivalent of Linear Inequality with One Variable

There are some rules about inequality, i.e. :

1. If both sides are added or subtracted by certain number, the sign of the inequality does not change.

Example :

both sides are subtracted by 6

2. If both sides are multiplied or divided by a positive number (non zero), the sign of the inequality does not change.

Example :

both sides are divided by 2

3. If both sides are multiplied or divided by a negative number (non zero), the sign of the inequality changes into the opposite.

Example :

both sides are divided by (-3)

the sign changes into the opposite

Exercise

Find the solution of the following inequalities.

1. 4.

2. 5.

3.

C. The application of Linear Inequality with One Variable

There are a lot of daily problems that need a linear inequality with one variable as a solution. Generally, you have to change the problems to mathematic sentence first. After that, you can already solve the problems.

Example

Mr Ahmad has a rectangle form of vegetables farm. The wide of the farm is X m and its length is (2x + 5) meters. He will put the bamboos around the farm as a fence. Determine the value of x so that he can put a bamboos 100 meters long!

Solution

He will put the bamboos as a fence 100 meters long. It means the perimeter is not more than 100 m. For example, the farm’s perimeter is K, so K 100.

both sides are subtracted by 10

both sides are divide by 6

Hence, in order that 100 m bamboos are enough as a fence, the value of is not more than 15 m.

Exercise

1. A computer shop has one million rupiahs profits for each computer that has been sold. How many computers to sell to get between 20 million and 25 million profits?

2. Mother bought a pizza in a circle form , she divides the pizza into 12 equal parts. Ali gets parts, Tono parts, and Anton parts. Is the rest of pizza bigger than of the whole pizza.

3. An employee will get bonuses if the shop has at least 5 million profits each moth. This year, the shop has Rp 48.000.000 profits. Will the employee get the bonuses?

4. A rectangle has 4 meter long more than its wide. Determine the are of the rectangle if the perimeter is 32 m!

5. A bamboo of 15 meters long is cut into two parts. The first part is 3 meters longer than the other. How long for each part of the bamboo ?

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Catatan: Artikel ini diperuntukan khusus bagi guru yang mempersiapkan diri untuk pbm matematika kelas bilingual atau kelas internasional dan bagi para mahasiswa yang sedang menempuh kuliah Bahasa Inggris II untuk Pendidikan Matematika

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