# Linear Equations

## Exercise 2.3 part 1

### Solve the following equations and check your results

Question 1: `3x=2x+18`

**Solution:** Given `3x=2x+18`

By transposing 2x to LHS we get:

`3x-2x=18`

Or, `x=18`

**CHECK:** Given equation is `3x=2x+18`

Substituting the value of x in LHS we get:

`3x=2xx18+18`

Or, `3x=36+18=54`

By dividing both sides by 3 we get:

`(3x)/(3)=(54)/(3)`

Or, `x=18` proved

Question 2: `5t-3=3t-5`

**Solution:** Given `5t-3=3t-5`

By transposing 3t to LHS and -3 to RHS we get:

`5t-3t=-5+3`

Or, `2t=-2`

By dividing both sides by 2 we get:

`(2t)/(2)=-2/2`

Or, `t=-1`

**CHECK:** Given equation is `5t-3=3t-5`

Substituting the value of t in LHS we get:

`5xx(-1)-3=3t-5`

Or, `-5-3=3t-5`

Or, `-8=3t-5`

Transposing -5 to LHS we get:

`-8+5=3t`

Or, `3t=-3`

Dividing both sides by 3 we get:

`(3t)/(3)=-3/3`

Or, `t=-1` proved

Question 3: `5x+9=5+3x`

**Solution:** Given `5x+9=5+3x`

By transposing 3x to LHS and 9 to RHS we get:

`5x-3x=5-9`

Or, `2x=-4`

By dividing both sides by 2 we get:

`(2x)/(2)=-4/2=-2`

Or, `x=-2`

**CHECK:** Given equation is `5x+9=5+3x`

Substituting the value of x in RHS we get:

`5x+9=5+3xx(-2)`

Or, `5x+9=5-6=-1`

By transposing 9 to RHS we get:

`5x=-1-9=-10`

By dividing both sides by 5 we get:

`(5x)/(5)=(-10)/(5)`

Or, `x=-2` proved

Question 4: `4x+3=6+2x`

**Solution:** Given `4x+3=6+2x`

By transposing 2x to LHS and 3 to RHS we get:

`4x-2x=6-3`

Or, `2x=3`

By dividing both sides by 2 we get:

`(2x)/(2)=3/2`

Or, `x=3/2`

**CHECK:** Given equation is `4x+3=6+2x`

Substituting the value of x in RHS we get:

`4x+3=6+2xx3/2`

Or, `4x+3=6+3=9`

By transposing 3 to RHS we get:

`4x=9-3=6`

By dividing both sides by 4 we get:

`(4x)/(4)=6/4`

Or, `x=3/2` proved

Question 5: `2x-1=14-x`

**Solution:** Given `2x-1=14-x`

By transposing –x to LHS and -1 to RHS we get:

`2x+x=14+1`

Or, `3x=15`

By dividing both sides by 3 we get:

`(3x)/(3)=(15)/(3)`

Or, `x=5`

**CHECK:** Given equation is `2x-1=14-x`

By substituting the value of x in RHS we get:

`2x-1=14-4=9`

By transposing -1 to RHS we get:

`2x=9+1=10`

By dividing both sides by 2 we get:

`(2x)/(2)=(10)/(2)`

Or, `x=5` proved