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

2 Answers

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

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