Algebra Math Problem Solver For X


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Solving algebra requires you to be highly focused and creative both at the same time just like solving a puzzle and finding the missing pieces to fit in. Not everyone is creative and not everyone finds algebra interesting but still algebraic concepts are applied in everyday life.

To simplify your algebraic problems, Mathifai has come up with the solution. Our algebra math problem solver works best with all types of algebraic questions including quadratic equations, linear equations, inequalities, polynomials, exponents, factoring, functions, sequences and expressions.

Algebra math problem solver Mathifai
Algebra math problem solver Mathifai
Mathifai

How To Use Our Algebra Math Problem Solver?

Our algebra math problem solver is designed to create ease for our community and that too in simple steps.

Step 1: Enter Your Problem

Upon opening the tool, you will see a container for entering your question.

Step 2: Choose The Answer Format

Now choose your desired format whether you need the direct answer, detailed explanation or step-by-step solution.

Step 3: Click “Solve Problem” Button

After entering your query and hitting that “Solve Problem” button, the tool will give you the final answer in your desired output.

Follow-Up Questions

If you need further explanations or clarity in any step, then the integrated AI chatbot in this tool will help you out.

What Can Our Algebra Math Solver Do?

Our math solver for algebra tool is all-in-one solution and serves as the most effective tool for solving algebra math problems with steps. It works with the same accuracy in areas like:

  • nth term calculator
  • Pattern solver
  • Expression math solver
  • Solve for x math problems
  • Math algebraic expressions solver
  • Math properties solver
  • Math solver for sequence

Math Symbols

Our algebra math problem solver tool is equipped with all the symbols necessary to simplify algebraic expressions or solve equations. The common symbols that the tool can interpret are:

Name

Symbol

Plus

+

Minus

–

Multiply

*

Divide

÷

Equals

=

Not equal to

≠

Exponent / Power

^

Square root

√

Greater than

>

Less than

<

Greater or equal

≥

Less or equal

≤

Parentheses / brackets

[{( )}]

What is Algebra?

Algebra is the field of mathematics that is used to tell the relationship between multiple things that are changing and how the change of one value creates an impact on the other values. Algebra uses symbols to denote quantities that are not fixed and whose values are to be known.

Origin of Algebra

The name algebra is derived from an Arabic word “Al-Jabr” which means “restoration or completion of broken parts”. A famous mathematician Muhammad Ibn-e-Musa Al-Khwarizmi laid the foundation of algebra in the 9th century (around 820 AD) and he is known as the father of algebra.

Fundamental Concepts

Before proceeding to understand algebra or using our algebra math problem solver tool, it is crucial to know the fundamental concepts of algebra and basic terminologies.

Understanding Variables

Variables are defined as the letters that are unknown in the equation or expression and whose value makes sense to the whole equation.

3x+4=133x+4=13

Here, ‘x’ is the variable whose value is to be calculated.

Understanding Constants

Constants are defined as the fixed value numbers that do not change and are present in the expression or equation. These constants can be positive or negative both.

For example, in the expression

9a2+2b−179a^2+2b-17

“-17” is the constant whose value is fixed and it will not change while solving the expression.

Understanding Expressions

Expressions are the combination of numbers and variables all on one side without the presence of “equals (=)” sign.

For example,

2x+102x+10

is an expression.

Understanding Equations

Equation is different from an expression as it is made up of two or more expressions with the presence of “equals (=)” sign. For example,

7x+4=9x−137x+4=9x-13

is an equation.

The Language of Algebra

Before moving to a new place it is recommended to learn the basic language of that particular place for understanding purpose. Same goes for jumping into any new field, first learn the basic language and terms of that field.

Operators

Operators are the basic arithmetic symbols that tell which mathematical operation (+, -, ×, ÷) to perform. In the expression,

2x+72x+7

The addition symbol ‘+’ is the operator.

Coefficients

These are the numbers that are directly multiplied with the variables. In the expression,

9x+79x+7

The number ‘9’ present with the variable ‘x’ is the coefficient.

Terms

A ‘term’ is defined as the basic unit of an algebraic expression. In a single expression there can be multiple terms separated by an addition (+) or subtraction (-) sign. For example,

7x+4a−137x+4a-13

There are 3 terms in this expression,

1st term = 7x

2nd term = 4a

3rd term = -13

What Are The Rules of Algebra?

The basic rules or properties of algebra are:

Mathifai Rules of Algebra

Commutative Property

a+b=b+aa+b=b+a

This rule of algebra says that the answer will remain the same no matter if we change the order of terms in the equation.

Example

4+3=3+44+3=3+4
7=77=7

Hence Proved!

Associative Property

(a+b)+c=a+(b+c)(a+b)+c=a+(b+c)

This property states that changing the grouping of terms will not change the final answer.

Example

(2+3)+5=2+(3+5)(2+3)+5=2+(3+5)
(5)+5=2+(8)(5)+5=2+(8)
10=1010=10

Hence Proved!

Distributive Property

a(b+c)=ab+aca(b+c)=ab+ac

The distributive property in algebra shows that if a number is being multiplied to a group of terms within the bracket, then that number will be multiplied by all the terms within the bracket.

Example

4(1+3)=4(1)+4(3)4(1+3)=4(1)+4(3)
4(4)=4+124(4)=4+12
16=1616=16

Hence Proved!

Identity Law

b+0=bb+0=b
a×1=aa ×1=a

This algebraic law states that specific operations with specific numbers do not change the identity of that number or variable. The specific operations are (addition and multiplication), while the specific numbers are (0 and 1).

Example

If the number ‘0’ is added to any number or variable, the original identity of that number or variable remains the same.

0+8=80+8=8

OR

0+x=x0+x=x

Similarly, if we multiply the number ‘1’ with any variable or number then in this case also the original identity remains unchanged.

1×7=71 ×7=7

OR

1×y=y1 ×y=y

Inverse Law

c+(−c)=0c+(-c)= 0
b×1b=1,b≠0b\times\frac{1}{b}=1,\quad b\ne0

This law of algebra tells us that the additive inverse of a number or variable will give ‘0’ as the result while the multiplicative inverse of the number or variable will give ‘1’ as the result.

Examples

i)7+(−7)=0i)\quad 7+(-7)=0
ii)a+(−a)=0ii)\quad a+(-a)=0
iii)4×1/4=1iii)\quad 4 × 1/4=1
iv)x×1/x=1iv)\quad x × 1/x=1

How To Simplify Algebraic Expressions?

Solving algebraic expressions require to combine like terms first and then applying different arithmetic operations to bring the expression in its simplest form.

Combining Like Terms

Like terms are the terms having same variables.

Example

4x2+7x−2x2+9x+54x^2+7x-2x^2+9x+5

Here the like terms are:

4x2and−2x24x^2 \quad \text{and} \quad -2x^2 \\[1em]
7xand9x7x \quad \text{and} \quad 9x

So combining these like terms will look like this

4x2−2x2+7x+9x+54x^2-2x^2+7x+9x+5
=2x2+16x+5=2x^2+16x+5

This is the final simplest version of the expression.

Simplifying Complex Expressions

There could be scenarios where the student is required to solve complex expressions as well having parentheses and exponents so let’s look at practical example for this.

Example

2x(x+3)+3(x−7)2x(x+3)+3(x-7)

Firstly, we will solve parentheses and multiply 2x with the first set of parentheses and multiply 3 with the second set of parentheses.

2x2+6x+3x−212x^2+6x+3x-21

Then we will combine the like terms and solve them to get the final simplified expression.

2x2+9x−212x^2+9x-21

How To Solve Algebraic Equations?

Algebraic equations are solved with the same rules as expressions, but the goal here is to find value of the unknown variable that satisfies the equation. While solving an equation we stick to one rule, whatever operation is performed on one side of the equation, it must also be performed on the other side as well.

Objective of Solving Equations

The main objective of algebra is to find value of the unknown variables in the equation. Our math solver for algebra works best with all types of algebraic equations.

Solving One-Step Equations

y+9=10y+9=10

Subtract ‘9’ on both sides of the equation

y+9−9=10−9y+9-9=10-9
y=1y=1

Solving Two-Step Equations

5x−7=285x-7=28

Add ‘7’ on both sides of the equation

5x−7+7=28+75x-7+7=28+7
5x=355x=35

Now divide both sides by ‘5’ to get final value of “x”

5x5=355\frac{5x}{5}=\frac{35}{5}
x=7x=7

Solving Multi-Step Equations

3(z+5)−9=123(z+5)-9=12

First solve the parentheses by multiplying both terms inside the bracket by ‘3’.

3z+15−9=123z+15-9=12
3z+6=123z+6=12

Subtract ‘6’ on both sides of the equation.

3z+6−6=12−63z+6-6=12-6
3z=63z=6

Now divide both sides of the equation by ‘3’

z=2z=2

Solving Equations with Variables on Both Sides

9x+2=3x−19x+2=3x-1

Subtract ‘3x’ from both sides of the equation.

9x−3x+2=3x−3x−19x-3x+2=3x-3x-1
6x+2=−16x+2=-1

Subtract ‘2’ on both sides.

6x+2−2=−1−26x+2-2=-1-2
6x=−36x=-3

Divide both sides by ‘6’.

6x6=−36\frac{6x}{6}=\frac{-3}{6}
x=−12x=-\frac{1}{2}

What Are Inequalities?

Inequalities compare two expressions and show that one side is greater than, less than, greater than or equal to or less than or equal to the other side.

Solving Inequalities

3a−9<123a-9<12

Add ‘9’ on both sides first.

3a−9+9<12+93a-9+9<12+9
3a<213a<21

Now divide both sides by ‘3’.

3a3<213\frac{3a}{3}<\frac{21}{3}

Answer: All real numbers less than 7.

Algebra In The Real World

Many people find mathematics boring as they feel they are not going to use these mathematical formulas in their daily life. But the concept of algebra proves this wrong since finding unknown values is the basic concept of algebra and this concept is applied almost in every field and in daily life activities too.

Cooking

This is the most basic use of algebra in our daily life. Suppose the food is being prepared for 5 people and suddenly some guests arrived so the same food will require more ingredients to add so that it can serve those additional persons as well. To find this change in quantity of ingredients, algebra is used.

Interior Designing

If you are planning to place a small table in a room besides the bed then you will be calculating the available space first and the dimensions of that table to see if it could fit in there or not. Thus, to do this simple algebraic thinking is used to find the unknown.

Sports

Every sportsman uses algebra according to their nature of game. A runner calculates how fast he has to run to beat the opponent, a cricketer calculates how fast he should hit the shot for a sixer, a footballer calculates how fast he should kick the ball to pass it to his teammate.

Business Calculations

All business owners perform business calculations based on algebraic fundamentals like calculating the minimum selling price of a product to make a profit or avoid loss.

Benefits of Our Algebra Math Problem Solver

Using our algebra math problem solver will be beneficial for you in numerous ways. It will

  • Save your precious time
  • Enhance your learning experience
  • Easy to access anywhere
  • Boosts confidence
  • Serves as personal AI teacher

Conclusion

Our algebra math problem solver tool is designed to help you when you are stuck somewhere in solving algebraic questions, cross-check your answers, clear your concepts and get help anytime anywhere.

FAQs

Solving algebraic expression requires to sort like terms together first, then performing operations on variables and constants individually to find the unknown.

The golden rule of algebra is to apply what you are performing on one side of the equation to the other side as well.

Yes our algebra math problem solver is highly helpful and accurate for students willing to get help with their algebra homework.