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Pre Algebra Equations

Any algebraic expression which two sides partitioned with an equal to sign is called as an equation.
Two sides of an equation may be either algebraic expressions or one side as an algebraic expression and the other side as a real number.
The goal in solving an equation is to get a variable by itself on one side of equation and a number on the other side. Depending upon the complexity of an equation number of steps while solving an equation would change. There are different types of equations based on their number of steps and the operations involved, they are single step equation with addition, a single step equation with subtraction, single step equation with multiplication, multi-step equation with addition and multiplication.

Let us discuss all the equations one by one:
1. Single step equation by addition - The General form of the single step equation by addition is: x + a = b for any real a and b. To get x itself on the left side we subtract ‘a’ from both sides which gives, x = b – a. Here the value of x is b – a.

2. A single step equation with subtraction - General form of single step equation with subtraction is x – a = b for any real a and b. To get x itself on the left side we add a on both sides which gives, x = b + a. Here the value of x is b + a.

3. A single step equation with multiplication - General form of single step equation with multiplication is a * x = b for any real a and b. To get x itself on the left side we divide both sides by a, which gives, $x = $$\frac{b}{a}$. Here the value of x is $\frac{b}{a}$.

4. Multi-step equation with addition - General form of multi-step equation with addition or subtraction and multiplication is, a * x – b = c or a * x + b = c. To isolate ‘x’ we first add or subtract b from both sides. This yields, a * x = c + b or a * x = c – b. Again in order to get rid of a we divide both sides by ‘a’. So that we get, $x = $$\frac{(c+b)}{a}$ or $x = $$\frac{(c-b)}{a}$.

Solved Examples:

a. y + 5 = 10
Subtract 5 from both sides, we get
y = 10 – 5
Hence y = 5

b. z – 15 = 25
Adding 15 both sides, we get,
z = 25 + 15
Hence z = 40

c. 4 * x = 16
Divide both sides by 4, we get
X = 4

d. 2x + 5 = 15
We subtract 5 from both sides, we get
2x + 5 – 5 = 15 – 5
2x = 10

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