Problem: Simplify the expression 6(3x - 4 ÷ 3) = 5x.

Solution:

To simplify the given expression, we need to follow the order of operations (PEMDAS/BODMAS). This means we need to perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

Simplifying inside the parentheses:

We have 3x - 4 ÷ 3 inside the parentheses. Let's simplify it step by step:

1. Start with division: 4 ÷ 3 = 1.33 (rounded to two decimal places).
2. Now substitute the result: 3x - 1.33.

Multiplication:

Now, let's simplify the expression 6(3x - 1.33):

1. Apply the distributive property: 6 * 3x - 6 * 1.33.
This gives us 18x - 7.98.

Combining like terms:

Now we have 18x - 7.98 = 5x. To solve for x, we need to combine like terms:

1. Subtract 5x from both sides of the equation: 18x - 5x - 7.98 = 0.
This gives us 13x - 7.98 = 0.

Isolating the variable:

To isolate the variable x, we need to get rid of the constant term (-7.98) by adding it to both sides of the equation:

1. Add 7.98 to both sides: 13x - 7.98 + 7.98 = 0 + 7.98.
This simplifies to 13x = 7.98.

Dividing both sides by the coefficient of x:

To solve for x, we divide both sides of the equation by the coefficient of x (13):

1. Divide both sides by 13: 13x/13 = 7.98/13.
This simplifies to x = 0.6138 (rounded to four decimal places).

Final Answer: The value of x that satisfies the equation 6(3x - 4 ÷ 3) = 5x is approximately x = 0.6138.