Useful Methods For How To Solve x with Examples.

Useful Methods For How To Solve x with Examples.

Hey! Are you also the one who is afraid of dealing with algebra! 

Well! Many students get scared after hearing the name of Mathematics. Particularly when they get to know they have to solve algebraic equations.

Moreover, students also do not know how to solve an algebraic equation. I was also the one who never knew how to solve x. If you also do not know how to deal with algebraic equations, Don’t Worry! We are here to Statistics Assignment Help equations to you. So, without wasting time, Let’s get started!

Before knowing the methods, first, you should know the basic meaning of an algebraic equation.

So, do you know what the algebraic equation is? If not, take a look at the basic meaning of the algebraic equation:

An algebraic equation is a mixture of words by the functions such as Addition, Subtraction, Multiplication and Division, etc.

  • For Example:

Look at these equations:

  1. 12x+6, 
  2. 10y, 
  3. 2x+5y+z
  4. 4x=y,
  5. 10x-5

Confused about what these terms indicate? Don’t be confused; all these expressions are called ALGEBRAIC EQUATION.

Additionally, it acts as a centre point of arithmetic. Algebraic equations stimulate students and trainees to get familiar with advanced maths such as Geometry and Topology, Arithmetic, Calculus and Analysis, Number theory, Dynamical systems and differential equations.

Methods For How To Solve x.

# Method 1: Linear Equation

So, How to solve x? The first and easy method to solve equations is Linear Equation.Take a look at it’s steps:

Step 1: Jot down the Problem. 

For example-

  • 2^2 (x+2)+8-5= 35

Step 2: Settle the exponent. 

Solve the expression by using order BODMAS, which stands for 

    • B-Brackets
  • O-Orders (powers/roots), 
  • D-Division
  • M-Multiplication
  • A-Addition
  • S-Subtraction.

 Remember! You cannot start solving it with the bracket because x is in the bracket. first solve with exponent 2^2, which means 2*2= 4

  • 4(x+2)+8-5= 35

Step 3: Multiply the terms: 

Separate 4 into (x+2). Here’s How.

  • 4x +8+8-5=35

Step 4: Add and Subtract the terms: 

 Add and subtract remaining digits. Here’s How.

  • 4x+ 16-5=35
  • 4x+11=35
  • 4x=35-11
  • 4x=24

Step 5: Distribute the Variable: 

Divide both sides of the expression by 4. It will result in finding out the value for x.

  • 4x=24
  • x=24/4
  • x=6

Step 6: Re-check Work:

  • 4(x+2)+8-5= 35
  • 4(6+2)+8-5=35
  • 4(8)+8-5=35
  • 32+8-5=35
  • 35=35


# Method 2: With Powers

Step 1: Jot down the Problem. 

Suppose you have an equation where the x term contains power:

For example

  • 2x^2+10=42

Step 2: Separate the terms with the power:

Now, put constant terms at the right side of the equation, and terms with power should be on the left side of the expression. Subtract 10from both sides of the equation. Here’s How.

  • 2x^2+10-10=42-10
  • 2x^2=32

Step 3: Separate the variable with the power by dividing both sides by the factor of the x.

 In this case, 2 is the factor of x, do a division from both sides of the equation by 2 to remove it. Here’s how:

  • (2^2)/2 = 32/2
  • x^2 = 16

Step 4: Take the common factor of both sides of the equation:

 Taking the common factor from both sides of the expression will remove it. Now you have only x on the left side and ± square root of 4 on the right side. Hence, 

  • x = ±4

Step 5: Re-check the work.

 Put x = 4 and x = -4 in the real equation to check the answer is true.

  • 2x^2+10=42
  • 2*4^2+10=42
  • 2*16+10=42
  • 32+10=42
  • 42=42


# Method 3: By Fractions


Step 1: Jot down the Problem. 

Suppose you have the following problem-

  • (x+2)/6=3/2

Step 2: Cross Multiply the terms

Multiply the numerator of each fraction by the denominator of another fraction. Multiply the first numerator (x+2) by the second denominator, 2, to obtain 2x+4 on the left side. Now multiply the second numerator, 3, by the first denominator, 6, to receive 18 on the right side of the equation. Here’s How:

  • (x+2)/6=3/2
  • (x+2)*2=3*6
  • 2x+4=18

Step 3: Merge the same terms. 

Merge the constant terms to subtract 4 from each side of the expression. Here’s How:

  • 2x+4=18
  • 2x=18-4
  • 2x=14

Step 4: Separate the variable with the power by dividing both sides by the factor of the x. 

Do a division 2x and 14 by 2, x-factor, to find a solution for x. 2x/2=x and 14/2=7. 

Hence, the value for x=7.

Step 5: Re-check the work. 

Put x=7 in the actual equation to check the answer.

  • (x+2)/6=3/2
  • (7+2)/6=3/2
  • (9)/6=3/2
  • 9*2=3*6
  • 18=18                    


Final words:

In this blog, we discussed the basic meaning and valuable methods for solving x. In addition to this, we have explained the methods briefly with step-by-step and examples so that students feel easy to read and understand. The most frequently used methods in algebraic equations are Linear Equation, With Powers, By Fractions. We hope that our blog will become very helpful for you, and it will also clear all your doubts regarding how to solve x.

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