One-step Linear Equations - Solved Examples

The following are some problems and their solutions of solving one-step linear equations.

Solved Example 1

`x + 6 = 7`

Solution

Write the original equation,
`x + 6 = 7`
Subtract 6 from both sides of the equation,
`x + 6 - 6 = 7 - 6`
Simplify the LHS and RHS,
`x = 1`
Thus, `x = 1` is the answer to the equation `x + 6 = 7`

Solved Example 2

`x - 4 = 2`

Solution

Write the original equation,
`x - 4 = 2`
Add 4 to both sides of the equation,
`x - 4 + 4 = 2 + 4`
Simplify the LHS and RHS,
`x =6`
Thus, `x = 6` is the answer to the equation `x - 4 = 2`

Solved Example 3

`2x = 10`

Solution

Write the original equation,
`2x = 10`
Divide throughout by 2,
`(2x)/2 = 10/2`
Simplify the LHS and RHS,
`x = 5`
Thus, `x = 5` is the answer to the equation `2x = 10`

Solved Example 4

`2x = 10 + x`

Solution

Write the original equation,
`2x = 10 + x`
Subtract `x` from both sides of the equation,
`2x - x = 10 + x - x`
Simplify the LHS and RHS,
`x = 10`
Thus, `x = 10` is the answer to the equation `2x = 10 + x`

Solved Example 5

`x - 5 = -6`

Solution

Write the original equation,
`x - 5 = -6`
Add 5 to both sides of the equation,
`x - 5 + 5 = -6 + 5`
Simplify the LHS and RHS,
`x = -1`
Thus, `x = -1` is the answer to the equation `x - 5 = -6`

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