Buksis-4.2 Revisi Akhir

4.2 What are you going to learn? To define a linear equation with one variable To make a model to state an equation To understand Solution and Solution Set

Think and discuss. A circus has 3 male and 3 female tigers. a) If the keeper feeds 39 kg of meat to the tigers each day and each tiger gets the same portion, what is the weight of meat fed to each tiger everyday?

Key Terms : • • •

equation linear equation with one variable solution and Set solution

Picture 4..4

b) If each tiger eats m kg of meat everyday, and the meat eaten by all tigers is 45 kg, write down an open sentence related to the weight of meat eaten by all tigers. How many kg of meat are eaten by six female tigers? c) If a male tiger eats meat twice as much as a female tiger, and the meat eaten by all tigers is 36 kg, how many kilograms of meat are eaten by six male tigers? In the tiger problems: • If one tiger eats m kg, then the relation is 6m = 45. • The value of m is unknown. Therefore, m is a variable. An open sentence that uses the sign “=” is called an equation. • If the highest power of the variable in an equation is 1, then that equation is called a linear equation.

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Consider the following equations. Determine which ones are linear equations with one variable? Give the reasons. a) p - 12 = 5 b) t + r = 28 c) h2 = 16 d) 2k – 3 = k + 7

Think and discuss. To celebrate the Independence Day of Indonesia, students of “SMP Association” and students of “SMP Reconciliation” held a competition in the square of the district. They went to the square of the district by car and bicycle. Students of “SMP Association” needed three cars and six bicycles. Students of “SMP Reconciliation” needed two cars and seven bicycles. The number of students in each car was the same.

If the total number of the students of those two schools was 88, (a) how many cars were used to go to the square of the district? (b) how many students went to the square of the district by bicycle? (c) how many students were there in each car?

Look at the tiger problem again. The equation we get is 6m = 45. If m is substituted by five, then the sentence becomes 6 x 5 = 45 and it is

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false. If m is substituted by 6, then the sentence becomes 6 x 6 = 45 and it is false. If m is substituted by 7, then the sentence becomes 6 x 7 = 45 and it is false. If m is substituted by 7 1 , then the sentence becomes 2 6 x 7 1 = 45 and it is true. Is there any value of m to 2 make the sentence true?

The value to make the equation becomes true is called a solution of the equation. Therefore, the solution of the equation 6m = 45 is 7 1 . 2

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1.

In the following sentences, determine which one

is a linear equation with one variable and which one is a non linear equation with one variable. Give reason. a. 3s = 4 – s

f. x2 – x = 0

b. –5t > t + 2

g. k ³ -5k +3

c. m = 2n – 5

h. x – y = 7

d. x = 9 – 3x

i. 2s + s + 9

e. y + 5 = -1

j. 5m = 2m + 5

2. Write T in the bracket if the statement is true and write F if the statement is false (do it by replacing the value of x in the equation). a. 4 is a solution of –2x + 4 = x (. . . ) b. –3 is not a solution of 2x – 3 = 9

(...)

c. 5 is a solution of 5x – 10 = x + 10 ( . . . ) d. 0 is a solution of x – 3 = 2x – 3 ( . . . ) e. –1 is not a solution of 3x + 3 = 0 ( . . . ) f.

3 is a solution of 4x – 5 = 8x + 1 ( . . . ) 4

g. -

3 is a solution of 5x + 6 = -10x – 3 ( . . . ) 5

3. Write examples of open sentences that can be represented by the following linear equation. a. 5 − x = 3

c. 5x + 3 = 3x + 9

b. x – 2 = 3x + 4

d. 8 – x = 2x – 1

4. Write a linear equation with one variable for each of the following statements.

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a. If Rp500.00 is added to Fia’s money, it will become Rp 5,000.00. b. After 7 books are taken by Ida, Ifa has 12 books left. c. If Fitri’s money is multiplied by 2, it will become Rp 15,000.00. d. If Dani’s money is given to his two younger brothers, each of them will have Rp 3,500.00. e. After it is added Rp 50,000.00, Mother’s money becomes Rp75,000.00.

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