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

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 #2

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 #3

Solve for x x :

5x3=45 5x \cdot 3 = 45

Video Solution

Step-by-Step Solution

To solve the equation5x3=45 5x \cdot 3 = 45 , follow these steps:

1. First, identify the operation needed to solve forx x . In this case, we have a multiplication equation.

2. Therefore, we divide both sides of the equation by 15 (since 5×3=15 5 \times 3 = 15 ) to isolate x x :

x=4515 x = \frac{45}{15}

3. Calculate x x :

x=3 x = 3

Answer

x=3 x=3

Exercise #4

Solve for X:

10+3x=19 10+3x=19

Video Solution

Step-by-Step Solution

To solve the equation 10+3x=1910 + 3x = 19, follow these steps:

  • Step 1: Subtract 10 from both sides of the equation to begin isolating xx:
  • 10+3x10=191010 + 3x - 10 = 19 - 10
  • This simplifies to 3x=93x = 9.
  • Step 2: Divide both sides by 3 to solve for xx:
  • 3x3=93\frac{3x}{3} = \frac{9}{3}
  • This reduces to x=3x = 3.

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

Answer

3

Exercise #5

Solve for X:

248x=2x 24-8x=-2x

Video Solution

Step-by-Step Solution

To solve the equation 248x=2x 24 - 8x = -2x , we need to isolate x x . Follow these steps:

  • Step 1: Move all terms involving x x to one side of the equation. Add 8x 8x to both sides to get:
    24=8x2x 24 = 8x - 2x
  • Step 2: Simplify the equation by combining like terms on the right:
    24=6x 24 = 6x
  • Step 3: Solve for x x by dividing both sides by 6:
    x=246 x = \frac{24}{6}
  • Step 4: Simplify the result:
    x=4 x = 4

Therefore, the solution to the problem is x=4 \mathbf{x = 4} .

Answer

4

Exercise #6

Solve for X:

2+x5=43 2 + x - 5 = 4 - 3

Video Solution

Step-by-Step Solution

To solve2+x5=43 2 + x - 5 = 4 - 3 , we first simplify both sides:

Left side:
25+x=3+x 2 - 5 + x = -3 + x

Right side:
43=1 4 - 3 = 1

Now the equation is 3+x=1 -3 + x = 1 .

Add 3 to both sides:
x=1+3 x = 1 + 3

So,x=4 x = 4 .

Answer

4

Exercise #7

Solve for X:

33x11x=66 33x-11x=66

Video Solution

Step-by-Step Solution

To solve the given linear equation 33x11x=66 33x - 11x = 66 , we will follow these steps:

  • Simplify the equation by combining like terms.
  • Isolate the variable x x to find its value.

Here's how we approach it:

Step 1: Combine like terms on the left-hand side of the equation.

We have 33x11x 33x - 11x . By combining these terms, we calculate:

33x11x=(3311)x=22x 33x - 11x = (33 - 11)x = 22x .

Our equation now simplifies to 22x=66 22x = 66 .

Step 2: Isolate x x by dividing both sides of the equation by 22.

When we divide both sides of the equation by 22, we get:

x=6622 x = \frac{66}{22} .

By performing the division, we find x=3 x = 3 .

Therefore, the value of x x that satisfies the equation 33x11x=66 33x - 11x = 66 is x=3 x = 3 .

Answer

3

Exercise #8

Solve for X:

3x=106 3 - x = 10 - 6

Video Solution

Step-by-Step Solution

First, simplify the right side of the equation:
106=4 10 - 6 = 4
Hence, the equation becomes 3x=4 3 - x = 4 .
Subtract 3 from both sides to isolate x x :
3x3=43 3 - x - 3 = 4 - 3
This simplifies to:
x=1 -x=1
Divide by -1 to solve forx x :
x=1 x=-1
Therefore, the solution is x=1 x = 1 .

Answer

-1

Exercise #9

Solve for X:

3+x+1=62 3 + x + 1 = 6 - 2

Video Solution

Step-by-Step Solution

To solve 3+x+1=62 3 + x + 1 = 6 - 2 , we first simplify both sides:

Left side:
3+1+x=4+x 3 + 1 + x = 4 + x

Right side:
62=4 6 - 2 = 4

Now the equation is 4+x=4 4 + x = 4 .

Subtract 4 from both sides:
x=44 x = 4 - 4

So, x=0 x = 0 .

Answer

0

Exercise #10

Solve for X:

3+x2=73 3 + x - 2 = 7 - 3

Video Solution

Step-by-Step Solution

First, simplify both sides of the equation:

Left side: 3+x2=1+x 3 + x - 2 = 1 + x

Right side: 73=4 7 - 3 = 4

So the equation becomes:

1+x=4 1 + x = 4

Next, isolate x x by subtracting 1 from both sides:

1+x1=41 1 + x - 1 = 4 - 1

This simplifies to:

x=3 x = 3

Answer

3

Exercise #11

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 #12

Solve for X:

3x5=10 3x-5=10

Video Solution

Step-by-Step Solution

To solve the equation 3x5=103x - 5 = 10, we follow these steps:

  • Add 55 to both sides of the equation to eliminate the 5-5:
    3x5+5=10+53x - 5 + 5 = 10 + 5
    Simplifies to:
    3x=153x = 15
  • Next, divide both sides of the equation by 33 to solve for xx:
    3x3=153\frac{3x}{3} = \frac{15}{3}
    This results in:
    x=5x = 5

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

Answer

5

Exercise #13

Solve for X:

3x+7=5 3-x+7=5

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Simplify the given equation by combining like terms.
  • Step 2: Isolate the variable x x on one side of the equation.
  • Step 3: Solve the resulting simplified equation for x x .

Now, let's work through each step:

Step 1: Simplify the given equation:

The original equation is: 3x+7=5 3 - x + 7 = 5 .

Combine like terms on the left side of the equation:

3+7=10 3 + 7 = 10 , so the equation becomes:

10x=5 10 - x = 5 .

Step 2: Isolate the variable x x :

Subtract 10 from both sides of the equation to move the constant term:

x=510 -x = 5 - 10 .

Simplify the right side:

x=5 -x = -5 .

Step 3: Solve for x x :

Multiply both sides of the equation by 1-1 to solve for x x :

x=5 x = 5 .

Therefore, the solution to the problem is x=5 x = 5 .

Answer

5

Exercise #14

Solve for X:

5x=124 5 - x = 12 - 4

Video Solution

Step-by-Step Solution

First, simplify the right side of the equation:
124=8 12 - 4 = 8
Hence, the equation becomes 5x=8 5 - x = 8 .
Subtract 5 from both sides to isolate x x :
5x5=85 5 - x - 5 = 8 - 5
This simplifies to:
x=3 -x=3
Divide by -1 to solve for x x :
x=3 x=-3
Therefore, the solution is x=3 x=-3 .

Answer

-3

Exercise #15

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