What is the solution to the equation `2\left(2x+1\right)\ =\ 3\left(3x+4\right)`?

Answer 1

To solve this equation, we will distribute on both sides and combine like terms:

Starting with the left side of the equation:
2 * 2x = 4x
2 * 1 = 2

So the left side simplifies to:
4x + 2

Now, moving to the right side of the equation:
3 * 3x = 9x
3 * 4 = 12

So the right side simplifies to:
9x + 12

Now we have the equation:
4x + 2 = 9x + 12

To isolate the variable x, we can get rid of the constants on the right side by subtracting 9x and 12 from both sides:
4x - 9x + 2 - 12 = 9x - 9x + 12 - 12
-5x - 10 = 0

To solve for x, we can add 10 to both sides:
-5x - 10 + 10 = 0 + 10
-5x = 10

Finally, we can divide both sides by -5 to solve for x:
(-5x)/-5 = 10/-5
x = -2

Therefore, the solution to the equation is x = -2.