How to Use Algebra

Algebra:

Algebra word problems are very useful to answer real-life problems. Remember the famous words of Albert Einstein

Definition:

That branch of math which treats of the relations and properties of quantity by means of letters and other symbols.

A branch of mathematics in which signs, 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.


How to use Algebra:


An algebraic expression is every combination of variables and constants with mathematical operations (addition, subtraction, multiplication, division, roots and powers). Writing algebraic expressions is a method of determining and combining constants, variables, and math convention using the order of operations. The next shows how to put in writing algebraic expressions, with an example in parentheses.

Step 1:

Write down what the algebraic expression is to show. (A toy line has toys of 3 different sizes and both with a different price. Small costs $5, medium costs $10, and large costs $15. Write as an algebraic expression.)

Step 2:

Determine the constant(s). (5, 10, 15 for price of each size toy.)

Step 3:

Determine the variable(s). (x, y, z for the quantity of each size toy.)

Step 4:

Determine the operations that need to be done. (Multiply both prices by the quantity and find the sum total of all 3 sizes.)

Step 5:

Mingle the constants, variables, and operations using the conventions of the order of operations. This is the algebraic expression. (5x + 10y + 15z)

I have recently faced lot of problem while learning Division of Rational Numbers, But thank to online resources of math which helped me to learn myself easily on net.

Use Algebra expressions with detailed solutions:


Problem 1:

Answer the expression 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Solution:

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

-15x - 10 - x + 3 = -16x - 20 +13

-16x - 7 = -16x – 7

0 = 0

Problem 2:

Reduce the algebraic expression 2(a -3) + 4b - 2(a -b -3) + 5

Solution:

= 2(a -3) + 4b - 2(a -b -3) + 5

= 2a - 6 + 4b -2a + 2b + 6 + 5

= 6b + 5

Problem 3:

Reduce |x - 2| - 4|-6|

Solution:

= |x - 2| - 4|-6|

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

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

= -x -22

Problem 4:

Estimate f (2) - f (1), f(x) = 6x + 1

Solution:

f (2) - f (1) = (6*2 + 1) - (6*1 + 1)

= 6

Problem 5:

Answer the equation |-2x + 2| -3 = -3

Solution:

|-2x + 2| -3 = -3

|-2x + 2| = 0

x = 1