"How to Solve the Equation 2(x+5)=3(x-1)"

  Let's solve the linear equation `2(x+5)=3(x-1)` together.

Introduction: A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. In this case, our equation is 

2(x+5)=3(x-1).

Body:To solve this equation, You need to isolate the variable `x` on one side of the equation and all the constants on the other side. 

 Start by distributing the `2` and `3` on both sides of the equation: `2(x+5)=3(x-1)` becomes

 `2x + 10 = 3x - 3`. Next, Subtract `2x` from both sides to isolate the variable: '

2x + 10 - 2x = 3x - 3 - 2x`, 

which simplifies to

 `10 = x - 3`. 

Finally, add `3` to both sides to solve for `x`: 

`10 + 3 = x - 3 + 3`, which gives us

 `x = 13`.

Another example: Let's try solving another linear equation together: '4(x-2) = 5(x+1)`. 

First, You'll distribute the `4` and `5` on both sides of the equation:

 `4(x-2) = 5(x+1)` 

becomes 

`4x - 8 = 5x + 5`. 

Next, Subtract `4x` from both sides to isolate the variable: `4x - 8 - 4x = 5x + 5 - 4x`, 

which simplifies to 

`-8 = x + 5`. 

Finally, Subtract `5` from both sides to solve for `x`: 

`-8 - 5 = x + 5 - 5`, which gives us 

`x = -13`.

Conclusion: Solving linear equations involves isolating the variable on one side of the equation and all the constants on the other side. We can do this by performing the same operations on both sides of the equation until we have solved for the variable.

Practice exercises: Here are three practice exercises for you to try:

1. Solve for x: `6(x+2) = 7(x-3)`

2. Solve for y: `-4(y+1) = -5(y-2)`

3. Solve for z: `(z+6)/3 = (z-7)/4`

This post was written by Awah Aweh who is an experience teacher of mathematics and writes content for the internet. 

 For more on linear equations, contact me at https://awahconnections.blogspot.com/ contact