Give the Russian equivalents for the following words and expressions from the text.

symbolic, statement, identity, unknown, member, number, to consist in, satisfy, solve, to mean, root, conditional, value, solution, replace.

Find the answers to these questions by quickly reading the text.

1. What is an equation?

2. What does it mean to solve an equation?

Read and translate the text.

 

An equation is a symbolic statement that two expressions are equal. Thus x + 3 = 8 is an equation, stating that x + 3 equals 8.

There are two kinds of equations: conditional equations, which are generally called equations and identical equations which are generally called identities.

An identity is an equality whose two members (sides) are equal for all values of the unknown quantity (or quantities) contained in it.

An equation in one unknown is an equality which is true for only one value of the unknown.

To solve an equation in one unknown means to find values of the unknown that make the left member equal to the right member.

Any such value which satisfies the equation is called the solution or the root of the equation.

Two equations are equivalent if they have the same roots. Thus, x - 2 = 0 and 3x - 6 = 0 are equivalent equations, since they both have the single root x = 2. In order to solve an equation it is permissible to:

a) add the same number to both members;

b) subtract the same number from both members;

c) multiply both members by the same number;

d) divide both members by the same number with the single exception of the number zero.

These operations are permissible because they lead to equivalent equations.

Operations a) and b) are often replaced by an equivalent operation called transposition. It consists in changing a term from one member of the equation to the other member and changing its signs.

An equation of the form ax + b = 0 where a ≠ 0 is an equation of the first degree in the unknown x. Equations of the first degree are solved by the permissible operations listed in this text. The solution is uncomplete until the value of the unknown so found is substituted in the original equation and it is shown to satisfy this equation.

Find in the text English equivalents for the following Russian words and word combinations.

проверка, условное уравнение, выражение, уравнение первой степени, решение, неизвестная величина, корень, заменять, удовлетворять.

Match the words with their definitions.

equation	the same in size, quantity, value
equal	an amount or a number of smth.
identical	equal in value or amount
quantity	a factor in a given situation whose bearing and importance is not apparent
unknown	a statement showing that two amounts or values are equal

Now complete the sentences with the appropriate form of the words from exercise 6. One word is not used.

1. Ten plus twelve is ____ to twenty two, isn't it?

2. Is ___ a mathematical or physical term?

3. All these equations are ___, aren't they?

4. Which of you have solved the ___?

 

8. Which of the following statements are true or false?

1. An equation is a symbolic statement that two expressions are equal.

2. There’s only one kind of equations. It is called an identical equation.

3. An equation in one unknown is an equality which is true for various values of the unknown.

4. Two or more equations are equivalent if they have the same roots.

5. An equation of the form ax + b = 0, where a ≠ 0 is an equation of the first degree in the unknown x.

Answer the following questions.

1. How many kinds of equations exist in mathematics?

2.What is an identity?

3.An equation in one unknown is an equality which is true for only one value of the unknown, isn’t it?

4. What value is usually called the solution of an equation?

5. What equation is called the equation in one unknown?

6. What must one do to solve an equation of the first degree?

Compare identical and equivalent equations.

Speak about equations (in 8-10 sentences).

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