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