Solve and check the solution for 4(2x-3)=3(2x+6).

First, use the **Distributive Property **on both sides of the equation.

8x - 12 = 6x + 18

Then, add -6x to both sides.

2x - 12 = 18.

Then, add 12 to both sides.

2x = 30

Finally, divide by sides by 2.

x = 15

To check, substitute 15 in for x in the original equation and simplify.

4(2 * 15 - 3)=3(2 * 15 + 6)

4(30 - 3) = 3(30 + 6)

4(27) = 3(36)

108 = 108

The substitution worked, therefore the solution **x = 15** is correct.

We have to solve: 4(2x-3)=3(2x+6)

4(2x-3)=3(2x+6)

=> 8x - 12 = 6x + 18

=> 8x - 6x = 18 + 12

=> 2x = 30

=> x = 30/2

=> x = 15

Substituting x = 15 on the left hand side of the equation gives

4(2*15 - 3) = 108

Similarly substituting x = 15 on the right hand side of the equation gives 3(2*15 + 6) = 108

**This proves that x = 15 is a solution of the equation.**

First, we'll move all terms to the left side:

4(2x-3)-3(2x+6) = 0

Now, we'll remove the brackets:

8x - 12 - 6x - 18 = 0

We'll combine like terms:

2x - 30 = 0

2x = 30

x = 15

We'll plug in the value of x, in the given expression, to check if it holds:

4(2*15-3)=3(2*15+6)

4*(30-3) = 3*(30 + 6)

108 = 108

**Since the values of both sides are equal, for x = 15, therefore x = 15 is the solution of the equation.**

4 ( 2x - 3 ) = 3 ( 2x + 6 )

First, distribute the 4 and the 3

By distributing, you should get

**8x - 12 = 6x + 18 **now add 12 on both sides

By adding, you should get

**8x = 6x + 30 **now subtract 6x on both sides

By subtracting, you should get

**2x = 30 **now divide 2 on both sides

By dividing, you should get

**x = 15 **which is your answer

*CHECKING YOUR WORK*

4 ( 2 X 15 - 3 ) = 3 ( 2 X 15 + 6 )

4 ( 30 - 3 ) = 3 ( 30 + 6 )

4 ( 27 ) = 3 ( 36 )

108 = 108

**so x = 15 is your answer**