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Chapter 6: Problem 97

In Exercises 97-104, solve each equation. \(\left[(3+6)^{2} \div 3\right] \cdot 4=-54 x\)

Short Answer

Expert verified
The solution to the equation \( \left[(3+6)^{2} \div 3\right] \cdot 4=-54 x \) is \( x=-\frac{2}{3} \).

Step by step solution

01

Apply the Order of Operations

Begin by applying the order of operations (BIDMAS/BODMAS) in the equation: \(\left[(3+6)^{2} \div 3\right] \cdot 4=-54 x\). Let's simplify inside the parenthesis first, then square, next do the division and after that multiplication. This gives an equation: \((9)^2\div 3\cdot 4=-54x\).
02

Further Simplification

Next, continue to simplify the equation.\[\sqrt{81}\div 3\cdot 4=-54x\]\[27\div 3\cdot 4=-54x\]\[9\cdot 4=-54x\]This simplifies to:\[36=-54x\]
03

Solve for 'x'

Now, aim to isolate the variable \(x\). The variable can be isolated by dividing both sides of the equation by \( -54 \):\[\frac{36}{-54}=x\]
04

Simplification of 'x'

Perform the division to calculate the value of \(x\):\[x=-\frac{2}{3}\]

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