Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Algebra assessment will cover the four basic operations such as addition, subtraction, multiplication and division. The most important terms for algebra assessment are variables, constant,coefficients, exponents, terms and expressions. For Algebra assessment,we have to use the symbols and alphabets in place of unknown values to make a statement. Hence, algebra assessment causes the leads of Arithmetic.

**Example 1:**

Solve the equation for x, 2(4x - 7) = 26.

**Solution:**

2(4x - 7) = 26

(2 * 4x) – (2 * 7) = 26

8x - 14 = 26(add 14 on both sides)

8x – 14 + 14 = 26 + 14

8x = 40 (divide both sides by 8)

`(8x) / 8="40" / 8`

x = 5

**Example 2:**

. If a="-3" and b="4," then -5ab^{4}=?

**Solution:**

Put a="-3" and b="4" in -5ab^{4}

-5ab^{4} = (-5 * -3) * 4^{4}

-5ab^{4} = -5 * -3 * (4 * 4 * 4 * 4)

-5ab^{4} = 15 (16 * 16)

-5ab^{4} = 15 * 256

-5ab^{4} = 3840

**Example 3:**

Solve (-3ab^{3}) (4a^{2}b^{3})

**Solution:**

(-3ab^{3}) (4a^{2}b^{3})

= (-3 * 4) * (a * a^{2}) * (b^{3 }* b^{3})

**Note:**

^{ }**(a**^{m}) (a^{n}) = a^{m+n}**a=a**^{1}

= -12 * ( a^{1+2}) * (b^{3+3})

=-12a^{3}b^{6}** **

**Example 4:**

Solve `(-3ab3)/(4a^2b^3)`^{}

**Solution:**

`(-3ab^3) / (4a^2b^3)`

**Note:**

**1/a = a**^{-1}**a**^{-1 }= a**a**^{0}= 1

`((-3 )* (a * a^(-2))* (b^3 * b^(-3)) ) /4 `

`(-3*a^(1+(-2))*b^(3-3))/4`

`(-3 * a^-1 * b^0) / 4`

`(-3 * a^-1 * 1) / 4`

`(-3* a^-1) / 4`

`-3/(4a)`

**Example 5: **

Use quadratic formula for solving x^{2 }+ 8x +7=0

**Solution:**

Here** **a = 1, b = 8 and c = 7

Discriminant: b^{2}-4ac = 8^{2 }– 4 * 1 * 7 = 36

Discriminant (36) is greater than zero. The equation has two solutions.

x =`-b+-sqrt(b2-4ac)/(2a)`

x =`(-8+-sqrt(64-28))/(2*1) `

x_{1,2} = (-8 ± 6) / 2 * 1

or

x_{1} = `-2 / 2` = -1

x_{2} = `-14 / 2 ` = -7

or

x_{1,2} = -1, -7

**Problem 1:**

Solve the equation for x, x-39=3.

The answer is x = 42

**Problem 2:**

Solve the inequality for x**, **6x = 72

The answer is x = 12

**Problem 3:**

Solve 6x/2x^{2}

The answer is x = 3/x

**Problem 4: **

Use quadratic formula solver 2x^{2}+16x+14=0

The answer is x_{1} = -1 and x_{2}=-7

**Problem 5: **

Use factorizing method for solving 2x^{2}+16x+14=0

The answer is x_{1} = -1 and x_{2}=-7