1. Read the text and translate it Ukrainian.
Algebra sounds like a difficult concept. Don't worry-- it's not hard at all. The basic idea is that we have an equation that is balanced on both sides. Picture a scale in your head with the same values on each side, and you have a basic understanding of algebra.
Notice how there is a six on each side, and so they are equal and the scale is balanced? That is your first equation! You've probably realized too that we can perform operations on each side of the equation (scale). Writing 4+2 on one side and 3+3 on the other will keep the scale balanced.
Of course, you don't have to use addition. Any of the other arithmetic operations, like subtraction, multiplication, or division will work, as each side is equal to the other. We will now convert the picture of the scale into an equation. This is a simple process, and all you have to do is to place your two values on opposite sides of an equals sign.
The equation is useful in finding the value of a missing number. Say we had an equation like this:
The empty box indicates a missing number. This equation can be solved by adding 3+3 to get 6, and then recognizing that 4+2=6. The number 2 is the missing number.
The next step in algebra is learning about a variable. Variables are defined as numbers that can change value or represent a missing value. Variables are usually represented by letters of the alphabet, and for whatever reason x, y, and z are the most commonly used variables. Here's how our last equation would look using a variable:
Since we have a balanced equation, we can do anything to one side, but we have to do the same to the other side. For instance, we can add 1 to each side, resulting in 4+x+1=3+3+1. Adding 1 to only one side would create an inequality, which is not what we want.
The best way to solve is by isolating the variable on one side of the equation, so that we can tell what value it holds by looking at the other side of the equation, as in x=4. To do this, we must get rid of the 4. Since we can do anything to both sides of the equation, why not subtract 4 from each side?
On the left side of the equation, 4-4 is obviously 0, so we can get rid of that, and 3+3=6, minus 4 is 2, so we can write 2 in place of 3+3-4.
Remember- the goal is to get the variable alone by doing the same thing to each side. In an equation like 4x + 4 = 12, you would subtract 4 from each side to get 4x = 8. Divide each side by four and you've got x=2. Now you've got a basic understanding of algebra, and can solve equations like 7+x=14.
2: Fill in the gaps and translate the sentences.
The basic idea of algebra is that we have an _________that is balanced on both sides.
If you imagine a __________ with the same ____________on each side, you will have a basic understanding of algebra.
We can perform _____________on each side of the_________________.
The equation is useful in finding the value of a_____________________.
________________are numbers that can change value or represent a missing value.
Adding a number to only one side of the equation would create an ____________.
In an equation like 4x + 4 = 12, you would ___________4 from each side to get 4x = 8.