Question

Round the result to the nearest hundredth. Check the rounded solution. $$2.6(4.2 y-6.5)=-7.1 y-2.8$$

Short answer

\nIndeed, the short answer for \(y\) is \(0.78\), rounded to the nearest hundredth.

Step-by-step solution

Distribute Multiplication

Distribute 2.6 across \(4.2y - 6.5\) to remove the parentheses: \(2.6 \times 4.2y - 2.6 \times 6.5 = -7.1y - 2.8\)

Simplify Both Sides of the Equation

After distributing, you get \(10.92y - 16.9 = -7.1y - 2.8\). On one side of the equation, add \(7.1y\) to consolidate the \(y\) terms: \(10.92y + 7.1y = -2.8 + 16.9\)

Solve for y

After adding like terms, you get \(18.02y = 14.1\). Now, divide both sides by \(18.02\) to solve for \(y\): \(y = 14.1 / 18.02\)

Round to the Nearest Hundredth

When you divide \(14.1 / 18.02\), you get \(y = 0.7819093198999439\), which you need to round to the nearest hundredth. This results in \(y = 0.78\)

Check the Solution

To ensure the correctness of the solution, plug \(0.78\) back into the original equation for \(y\) and verify that both sides of the equation match. That is, \(2.6(4.2 \times 0.78 - 6.5)\) should equal \(-7.1 \times 0.78 - 2.8\)