Saltar la navegación

# Equations

There are two sides in an equation with an algebraic expression in each one.

Each monomial is a term of the equation.

“x” is called the variable or the unknown.

The degree of an equation is the biggest degree of its terms. If the degree is 1, we call it a linear equation and if the degree is 2 we call it a quadratic equation.

Examples:

· x2 – 3x + 1 = 5x -17 is a quadratic equation

· x + 5 – 3(x + 2) = 5x is a linear equation

Two equations are equivalent if they have exactly the same solutions.
3x = 6 is equivalent to x = 2

To solve an equation is to find the simplest equivalent equation that gives us the solution.

To obtain an equivalent equation we can do only two basic operations:

- Add or subtract the same expression in both sides of the equation.
- Multiply or divide by the same number (except zero) in both sides of the equality.

Example 1: To solve the equation   2 + x = 5
–We subtract 2 in both sides   2 + x – 2 = 5 – 2
–Then we obtain the solution        x = 3
Example 2: To solve the equation       3x = 18
–We divide by 3 in both sides Example 3: To solve the equation     2x + 5 = 9
– We subtract 5 in both sides   2x + 5 – 5 = 9 – 5
- We have  2x = 4 and we divide by 2 Exercise: Find the error Example 4: To solve the equation    x – 3 = -21
–We add 3 in both sides   x – 3 + 3 = – 21 + 3
–Then we obtain the solution        x = -18
Example 5: To solve the equation we multiply by 3 in both sides Example 6: To solve the equation  -3x + 5 = x+1
–We subtract x in both sides   -3x + 5 – x = x + 1 - x
–We have  -4x + 5 = 1 ;  we subtract 5:  -4x = -4
–We divide by -4: NOTE: As you can see, when we remove a number or an expression, it appears in the other side with the reverse operation: if it is adding, it appears subtracting; if it’s subtracting, it appears adding; if it’s multiplying, it appears dividing; and if it’s dividing, it appears multiplying.