Question

1. solve the equation: 19 - 2(3w - 5) = 15

Explanation:

Step1: Expand the bracket

First, we use the distributive property (also known as the distributive law) to expand the term \(-2(3w - 5)\). The distributive property states that \(a(b - c)=ab - ac\). So, applying this to \(-2(3w - 5)\), we get:

$$ -2\times3w-(-2)\times5=-6w + 10 $$

Now our equation \(19-2(3w - 5)=15\) becomes:

$$ 19-6w + 10=15 $$

Step2: Combine like terms

Next, we combine the constant terms on the left - hand side. The constant terms are \(19\) and \(10\). So, \(19 + 10=29\). Our equation now is:

$$ 29-6w=15 $$

Step3: Isolate the variable term

We want to get the term with the variable (\(-6w\)) by itself. To do this, we subtract \(29\) from both sides of the equation. Subtracting \(29\) from both sides:

$$ 29-6w-29=15 - 29 $$

Simplifying both sides, we have:

$$ -6w=-14 $$

Step4: Solve for \(w\)

To solve for \(w\), we divide both sides of the equation by \(-6\). So:

$$ w=\frac{-14}{-6}=\frac{7}{3} $$

Answer:

\(w = \frac{7}{3}\)