Question

How do you solve `3x-51=-2x+59`?

Answer 1

`x= 22`

Explanation:

1) Combine Like terms by transposition of terms. [Remember to reverse the signs when transposing]

`3x - 51 = - 2x + 59`

By combining like terms, you should get

`3x + 2x = 110 + 51`

`rArr 5x = 110`

2) Divide by `5` on both sides and you will get the answer.

`5x = 110`

`rArr x= 22`

Answer 2

22

Explanation:

This is a topic of mathematical transpositions. The main goal of transposing is grouping variables and constants on different sides for easier evaluation without disrupting the equality of the whole system/equation.

For this example, we can group all terms with the `x` variables at one side, let's say the left side and also group all constants or terms without variables on the right side.

This would specifically mean that `-2x` will be transposed onto the left side and `-51` will be transposed onto the right side. As a result, the equation will yield:
`3x+2x=59+51`

Simplifying,
`5x=110`

Solving for `x`;
`x=frac110 5=22`

Take note that the transposed terms `-2x` and `-51` have changed their signs after transposing. This is true to maintain the equality of the whole equation.

For example,
`5+8=13`
If we transpose `8` onto the other side of the equation, the whole equation becomes
`[5 =13-8]` or `[5=-8+13]`
And we can see that the equality of the whole equation is maintained. In essence, the mathematical operation performed in the transposition can be done by subtracting `8` (or adding `-8`) on both sides:
`(5+8)-8=(13)-8`
`5=13-8`