Algebra Problems and Solutions

Introduction to algerba solutions:

Algebra deals with symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.

The Algebra is the branch of mathematics concerned with the rules of operations that are based on terms, polynomials, expressions and algebraic structures or pre-algebra structure.

The example of arithmetic expression is: 3 + 4 = 3 + 4 in Algebra it would look like: x + y = y + x.

In this article discuss about using algebra problem solver.

Steps invovled in finding solutions in algebra are:

1) Work out what to remove to get "x = ..."

2) Remove it by doing in the opposite (adding is the opposite of subtracting)

3) Do that to both sides

Find Solutions of Examples Using Algebra:

Pro 1:Simplify the expression

3(a -3) + 5b - 2(a -b -3) + 10

Sol:

Step 1: Given the algebraic expression 3(a -3) + 6b - 2(a -b -3) + 10

Step 2: Multiply factors 3a - 9 + 6b -2a + 2b + 6 + 10

Step 3: Group like term is a – 8b+7

Pro 2: To solve the equation: 5x+10= 0

Sol:

Step 1:The given Equation is 5x+10 =0

Step 2: subtract 10 on the both sides

Step 3: 5x+ 10 -10= -10

Step 4:5x =-10

Step 5: divided by 5 on both side.

Step 6: `5x/5 = -10/5`

Step 7: x= -2

The solution is -2

Some more Examples with Algebra Solutions:

Pro 3:Solve the equation of: 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Sol:

Step 1: Given the equation of 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Step 2: Multiply the factors -15x - 10 - x + 3 = -16x - 20 +13

Step 3: Group like of term is -16x - 7 = -16x - 7

Step 4: Adding the 16x + 7 on the both side 0 = 0

Step 5: The above statement is true for all elements of x and therefore all real elements are solutions to the given equation.Looking out for more help on Help with Math Problems for Free in algebra by visiting listed websites.

Pro 4:Simplify the expression 2(a -3) + 4b - 2(a -b -3) + 5

Sol:

Step 1: Given the algebraic expression 2(a -3) + 4b - 2(a -b -3) + 5

Step 2: Multiply factors 2a - 6 + 4b -2a + 2b + 6 + 5

Step 3: Group like term is 6b + 5

Pro 5: To find the 5(4+3) +10

Sol:

Step 1: Give the equation is 5(4+3) +10

Step 2: multiply the both term 20 +15 +10

Step 3: Add the all term is 45

Pro 6: Evaluate 2x2 - y2 - z if x = 3, y = -1 and z = -2

Sol:

Substitute the values for the variables;

= 2(3)2 - (-1)2 - (-2)

= 2(9) - (1) - (-2)

= 18 - (1) + (+2)

= 17 + 2

= 19

Pro 7: If x <2 -="-" 2="2" 4="4" :=":" br="br" simplify="simplify" x="x">Sol:
Given the expression

|x - 2| - 4|-6|

If x < ;2 then x - 2 < 2 and if x - 2 < 2 the |x - 2| = -(x - 2).

Substitute |x - 2| by -(x - 2) and |-6| by 6 .

|x - 2| - 4|-6| = -(x - 2) -4(6)

= -x -22

Pro 8: Solve the equation

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Sol :

Given the equation

5(-3x - 2) - (x - 3) = -4(7x + 5) + 25

Multiply factors.

-15x - 10 - x + 3 = -28x - 20 +25

Group like terms

-16x - 7 = -28x +5

12x=12

x=1

Pro 9: Solve for y:   ax + by =c

Sol:
Subtract ax from both sides:

by = c - ax

Divide both sides by b:

y=  `(c-ax)/(b)`