The solution for an equation is a numerical value that, when inserted in the place of the unknown (or the variable), will render both members of the equation equal, that is, we will obtain a "true statement". In first degree equations with one unknown, there can only be one solution.

Example:

X1=5X - 1 = 5

Solution of an equation x-1=5

This is an equation with one unknown or variable indicated by the letter XX. The equation is composed of two members separated by the use of the equal sign = = . The left member is everything to the left of the sign = = , and the right member is everything to the right of the sign.

Our goal is to isolate the variable (or clear the variable) X X in order that it only remains in one of the members of the equation. In doing so we should be able to determine its value. In this article we will learn how to use the four mathematical operations(addition, subtraction, multiplication and division) to isolate the variable X X .

Practice Linear Equations (One Variable)

Examples with solutions for Linear Equations (One Variable)

Exercise #1

Solve the equation

5x15=30 5x-15=30

Video Solution

Step-by-Step Solution

We start by moving the sections:

5X-15 = 30
5X = 30+15

5X = 45

 

Now we divide by 5

X = 9

Answer

x=9 x=9

Exercise #2

4x:30=2 4x:30=2

Video Solution

Step-by-Step Solution

To solve the given equation 4x:30=2 4x:30 = 2 , we will follow these steps:

  • Step 1: Recognize that 4x:304x:30 implies 4x30=2\dfrac{4x}{30} = 2.

  • Step 2: Eliminate the fraction by multiplying both sides of the equation by 30.

  • Step 3: Simplify the equation to solve for xx.

Now, let's work through each step:

Step 1: The equation is written as 4x30=2\dfrac{4x}{30} = 2.

Step 2: Multiply both sides of the equation by 30 to eliminate the fraction:
30×4x30=2×30 30 \times \dfrac{4x}{30} = 2 \times 30

This simplifies to:
4x=60 4x = 60

Step 3: Solve for xx by dividing both sides by 4:
x=604=15 x = \dfrac{60}{4} = 15

Therefore, the solution to the problem is x=15 x = 15 .

Checking choices, the correct answer is:

x=15 x = 15

Answer

x=15 x=15

Exercise #3

Solve the equation

7x+5.5=19.5 7x+5.5=19.5

Video Solution

Step-by-Step Solution

To solve the given equation 7x+5.5=19.5 7x + 5.5 = 19.5 , we'll follow these steps:

  • Step 1: Eliminate the constant term from the left side by subtracting 5.5 from both sides of the equation.
  • Step 2: Simplify the equation after subtraction to isolate the term with x x .
  • Step 3: Use division to solve for x x .

Now, let's work through each step:

Step 1: Subtract 5.5 from both sides.

We have:
7x+5.55.5=19.55.5 7x + 5.5 - 5.5 = 19.5 - 5.5

This simplifies to:
7x=14 7x = 14

Step 2: Divide both sides by 7 to solve for x x .

So, we divide by 7:
7x7=147 \frac{7x}{7} = \frac{14}{7}

This simplifies to:
x=2 x = 2

Therefore, the solution to the problem is x=2 x = 2 .

Answer

x=2 x=2

Exercise #4

Solve the equation

20:4x=5 20:4x=5

Video Solution

Step-by-Step Solution

To solve the exercise, we first rewrite the entire division as a fraction:

204x=5 \frac{20}{4x}=5

Actually, we didn't have to do this step, but it's more convenient for the rest of the process.

To get rid of the fraction, we multiply both sides of the equation by the denominator, 4X.

20=5*4X

20=20X

Now we can reduce both sides of the equation by 20 and we will arrive at the result of:

X=1

Answer

x=1 x=1

Exercise #5

Solve the equation

8x10=80 8x\cdot10=80

Video Solution

Step-by-Step Solution

To solve this linear equation, we need to isolate the variable x x . Here are the steps to follow:

  • Step 1: Simplify the equation by dividing both sides by 10. This gives us:

8x1010=8010 \frac{8x \cdot 10}{10} = \frac{80}{10}

This simplifies to:

8x=8 8x = 8

  • Step 2: Now, isolate x x by dividing both sides by 8:

8x8=88 \frac{8x}{8} = \frac{8}{8}

This simplifies to:

x=1 x = 1

Therefore, the solution to the equation 8x10=80 8x \cdot 10 = 80 is

x=1 x = 1 .

Answer

x=1 x=1

Exercise #6

5x=0 5x=0

Video Solution

Step-by-Step Solution

To solve the equation 5x=0 5x = 0 for x x , we will use the following steps:

  • Step 1: Identify that the equation is 5x=0 5x = 0 .
  • Step 2: To solve for x x , divide both sides of the equation by 5.

Let's perform the calculation as outlined in Step 2:

5x=0 5x = 0

Divide both sides by 5 to isolate x x :

x=05 x = \frac{0}{5}

Simplifying, this gives:

x=0 x = 0

Therefore, the solution to the equation 5x=0 5x = 0 is x=0 x = 0 .

The correct answer is option 4: x=0 x = 0 .

Answer

x=0 x=0

Exercise #7

5x=1 5x=1

What is the value of x?

Video Solution

Step-by-Step Solution

To solve the equation 5x=1 5x = 1 , we need to isolate x x . Here are the steps:

  • Step 1: Start with the equation 5x=1 5x = 1 .
  • Step 2: Divide both sides of the equation by the coefficient of x x , which is 5, to isolate x x . This gives us:
  • 5x5=15\frac{5x}{5} = \frac{1}{5}
  • Step 3: Simplify the left side:
  • 5x5=x\frac{5x}{5} = x
  • Step 4: Write the simplified equation:
  • x=15x = \frac{1}{5}

    Therefore, the solution to the equation 5x=1 5x = 1 is x=15 x = \frac{1}{5} .

The correct answer choice is:

x=15 x = \frac{1}{5}

Answer

x=15 x=\frac{1}{5}

Exercise #8

Find the value of the parameter X:

x+5=8 x+5=8

Video Solution

Step-by-Step Solution

To solve the equation x+5=8x + 5 = 8, follow these steps:

  • Step 1: Start with the original equation:
    x+5=8x + 5 = 8.
  • Step 2: Subtract 5 from both sides of the equation to isolate xx:
    x+55=85x + 5 - 5 = 8 - 5.
  • Step 3: Simplify both sides:
    x=3x = 3.

Therefore, the solution to the equation is x=3x = 3.

The correct answer choice is: :

3

Answer

3

Exercise #9

Solve for X:

3+x=4 3+x=4

Video Solution

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Identify the given equation 3+x=4 3 + x = 4 .
  • Step 2: Use subtraction to isolate the variable x x .

Now, let's work through these steps:
Step 1: We have the equation: 3+x=4 3 + x = 4 .
Step 2: Subtract 3 from both sides of the equation to isolate x x :

3+x3=43 3 + x - 3 = 4 - 3

This simplifies to:

x=1 x = 1

Therefore, the solution to the equation is x=1 x = 1 .

Answer

1

Exercise #10

Solve for X:

5x=4 5-x=4

Video Solution

Step-by-Step Solution

To solve the equation 5x=45 - x = 4, we aim to isolate xx on one side of the equation.

We start by considering the equation:
5x=45 - x = 4

Step 1: Eliminate 5 from the left side to isolate terms involving xx. To do this, subtract 5 from both sides of the equation:

(5x)5=45(5 - x) - 5 = 4 - 5

Step 2: Simplify both sides:

x=1-x = -1

Step 3: To solve for xx, multiply or divide both sides by 1-1 to change the sign of xx:

1x=11-1 \cdot -x = -1 \cdot -1

This simplifies to:

x=1x = 1

Therefore, the solution to the equation 5x=45 - x = 4 is x=1x = 1.

The correct answer is x=1x = 1.

Answer

1

Exercise #11

Solve for X:

8x=5 -8-x=-5

Video Solution

Step-by-Step Solution

To solve the equation 8x=5 -8 - x = -5 , we'll isolate the variable x x by performing algebraic operations:

Step 1: Add 8 to both sides of the equation to eliminate the 8-8:

8x+8=5+8 -8 - x + 8 = -5 + 8

This simplifies to:

x=3 -x = 3

Step 2: To solve for x x , we need to change the sign of x x . Multiply both sides by 1-1:

x=3 x = -3

Therefore, the solution to the equation is 3\boxed{-3}.

Answer

3 -3

Exercise #12

Find the value of the parameter X

8x=5 -8-x=5

Video Solution

Step-by-Step Solution

To solve the given linear equation 8x=5 -8 - x = 5 , we will follow these steps:

  • Add 8 to both sides of the equation to isolate the term involving x x .
  • Subtract x x from both sides to further simplify; however, applying approach 1 directly cancels this step.
  • Multiply both sides by -1 to solve for x x .

First, let's add 8 to both sides of the equation:

8x+8=5+8 -8 - x + 8 = 5 + 8

This simplifies to:

x=13 -x = 13

To find x x , multiply both sides of the equation by -1:

x=13 x = -13

Therefore, the solution to the equation is x=13 x = -13 .

Answer

13 -13

Exercise #13

Solve for X:

5+x=3 -5+x=-3

Video Solution

Step-by-Step Solution

To solve the equation 5+x=3-5 + x = -3, we can follow these steps:

  • Step 1: We want to isolate x x on one side of the equation. Currently, it is subtracted by 5, so we'll eliminate the -5 by performing the operation of addition.
  • Step 2: Add 5 to both sides of the equation to cancel out the -5:
    5+x+5=3+5-5 + x + 5 = -3 + 5
  • Step 3: Simplify both sides:
    x=3+5x = -3 + 5
  • Step 4: Perform the arithmetic operation on the right side:
    x=2x = 2

Therefore, the solution to the problem is x=2 x = 2 .

Answer

2 2

Exercise #14

Solve for X:

5x=25 5x=25

Video Solution

Step-by-Step Solution

To solve the equation 5x=255x = 25, we will isolate xx using division:

  • Divide both sides of the equation by 5:
5x5=255 \frac{5x}{5} = \frac{25}{5}

After performing the division, we get:

x=5 x = 5

Thus, the solution to the equation is x=5 x = 5 .

Answer

5

Exercise #15

Solve for X:

6x=72 6x=72

Video Solution

Step-by-Step Solution

To solve for xx in the equation 6x=726x = 72, follow these steps:

Step 1: Identify the equation and the coefficient of xx.
The given equation is 6x=726x = 72, where the coefficient of xx is 6.

Step 2: Isolate xx by dividing both sides of the equation by the coefficient (6).
Perform the division: x=726x = \frac{72}{6}.

Step 3: Simplify the result.
Calculating 726\frac{72}{6}, we get x=12x = 12.

Therefore, the solution to the equation is x=12x = 12.

Answer

12