Question

solve for u.
5.8 + 5.2u = -2.3 + 6.1u
u = \boxed{}

Explanation:

Step1: Subtract \(5.2u\) from both sides

To isolate the variable terms, we subtract \(5.2u\) from each side of the equation \(5.8 + 5.2u=-2.3 + 6.1u\). This gives us \(5.8=-2.3 + 6.1u - 5.2u\). Simplifying the right - hand side, we combine like terms: \(6.1u-5.2u = 0.9u\), so the equation becomes \(5.8=-2.3 + 0.9u\).

Step2: Add 2.3 to both sides

To get the term with \(u\) alone on one side, we add 2.3 to both sides of the equation \(5.8=-2.3 + 0.9u\). So, \(5.8 + 2.3=0.9u\). Calculating the left - hand side, \(5.8+2.3 = 8.1\), and the equation is now \(8.1 = 0.9u\).

Step3: Divide both sides by 0.9

To solve for \(u\), we divide both sides of the equation \(8.1 = 0.9u\) by 0.9. Using the formula \(u=\frac{8.1}{0.9}\), we find that \(u = 9\).

Answer:

\(u = 9\)