Question

Solve the equation. Round the result to the nearest hundredth. $$ 6.1(3.1+2.5 x)=15.3 x-3.9 $$

Short answer

The solution \(x\) is -5.77.

Step-by-step solution

Expand the parentheses

The equation is \(6.1(3.1+2.5x) = 15.3x-3.9\). The first task is to expand the parentheses: \(6.1 \times 3.1 + 6.1 \times 2.5x = 15.3x-3.9\) which simplifies to \(18.91 + 15.25x = 15.3x - 3.9\) .

Group like terms

Next, group like terms together. This gives: \(3.95x = -22.81\) . In order to isolate \(x\), you need to divide both sides by 3.95. This gives: \(x = -22.81 / 3.95\).

Calculate division and round

Perform the division: \(x = -5.77\). The task demands that we round the result to the nearest hundredth, so there is no need for additional work here.