Linear Equations (One Variable) - Examples, Exercises and Solutions

Understanding Linear Equations (One Variable)

Complete explanation with examples

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 .

Detailed explanation

Practice Linear Equations (One Variable)

Test your knowledge with 42 quizzes

Solve for X:

\( 10+3x=19 \)

Examples with solutions for Linear Equations (One Variable)

Step-by-step solutions included
Exercise #1

Solve for X:

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

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

Video Solution
Exercise #2

Solve for X:

x3+5=82 x - 3 + 5 = 8 - 2

Step-by-Step Solution

First, simplify both sides of the equation:

Left side: x3+5=x+2 x - 3 + 5 = x + 2

Right side: 82=6 8 - 2 = 6

Now the equation is: x+2=6 x + 2 = 6

Subtract 2 from both sides to isolate x x :

x+22=62 x + 2 - 2 = 6 - 2

Simplifying gives:

x=4 x = 4

Answer:

4

Video Solution
Exercise #3

Solve for X:

x+42=6+1 x + 4 - 2 = 6 + 1

Step-by-Step Solution

First, simplify both sides of the equation:

Left side: x+42=x+2 x + 4 - 2 = x + 2

Right side: 6+1=7 6 + 1 = 7

Now the equation is: x+2=7 x + 2 = 7

Subtract 2 from both sides to isolatex x :

x+22=72 x + 2 - 2 = 7 - 2

Simplifying gives:

x=5 x = 5

Answer:

5

Video Solution
Exercise #4

Solve for X:

3x=106 3 - x = 10 - 6

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

Video Solution
Exercise #5

Solve for X:

8x=113 8 - x = 11 - 3

Step-by-Step Solution

First, simplify the right side of the equation:
113=8 11 - 3 = 8
Hence, the equation becomes 8x=8 8 - x = 8 .
Subtract 8 from both sides to isolate x x :
8x8=88 8 - x - 8 = 8 - 8
This simplifies to:
x=0 -x=0
Divide by -1 to solve for x x :
x=0 x = 0
Therefore, the solution is x=0 x = 0 .

Answer:

0

Video Solution

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