Question

Solve the equation. Round the result to the nearest hundredth. $$ 4.21 x+5.39=12.07(2.01-4.72 x) $$

Short answer

The solution to the equation is approximately \(x \approx 0.31\).

Step-by-step solution

Distribute

Multiply 12.07 by each term inside the parentheses on the right side of the equation. This gives: \[4.21x + 5.39 = 12.07 \cdot 2.01 - 12.07 \cdot 4.72x\]

Simplify

Perform the multiplication, then combine like terms:\[4.21x + 5.39 = 24.2607 - 57.0104x\] Combine like terms to form:\[61.2204x = 18.8707\]

Solve for x

To solve for x, divide both sides of the equation by 61.2204:\[x = 18.8707 \div 61.2204\]

Round to the nearest hundredth

Perform the division and round to the nearest hundredth to get the final result:\[x \approx 0.31\]