100÷(19+(15x-84)÷6)=4

To solve this equation, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Let's break down the steps:

Step 1: Simplify the expression inside the parentheses. 15x - 84

Step 2: Divide the simplified expression by 6. (15x - 84) ÷ 6

Step 3: Add 19 to the result of step 2. 19 + (15x - 84) ÷ 6

Step 4: Divide 100 by the result of step 3. 100 ÷ (19 + (15x - 84) ÷ 6)

Now, let's solve the equation step by step:

Step 1: Simplify the expression inside the parentheses. 15x - 84

Step 2: Divide the simplified expression by 6. (15x - 84) ÷ 6 = (15x)/6 - 84/6 = (5/2)x - 14

Step 3: Add 19 to the result of step 2. 19 + (5/2)x - 14 = (5/2)x + 5

Step 4: Divide 100 by the result of step 3. 100 ÷ ((5/2)x + 5) = 4

To find the value of x, we need to solve the equation

4 = (5/2)x + 5

Subtract 5 from both sides:

4 - 5 = (5/2)x -1 = (5/2)x

Now, divide both sides by (5/2):

(-1) / (5/2) = (5/2)x / (5/2) (-2/5) = x

Therefore, the value of x in the given equation is -2/5.