Question

solve the equation. simplify your answer if possible. 10 = 7 + 2(5z + 3)

Explanation:

Step1: Distribute the 2

First, we use the distributive property to expand \(2(5z + 3)\). The distributive property states that \(a(b + c)=ab+ac\), so here \(a = 2\), \(b = 5z\), and \(c = 3\).
\[

$$\begin{align*} 10&=7 + 2\times5z+2\times3\\ 10&=7 + 10z+6 \end{align*}$$

\]

Step2: Combine like terms

Next, we combine the constant terms on the right - hand side. The like terms \(7\) and \(6\) can be added together.
\[

$$\begin{align*} 10&=10z+(7 + 6)\\ 10&=10z + 13 \end{align*}$$

\]

Step3: Subtract 13 from both sides

To isolate the term with \(z\), we subtract \(13\) from both sides of the equation.
\[

$$\begin{align*} 10-13&=10z+13 - 13\\ - 3&=10z \end{align*}$$

\]

Step4: Divide both sides by 10

Finally, we divide both sides of the equation by \(10\) to solve for \(z\).
\[
z=\frac{-3}{10}=- 0.3
\]

Answer:

\(z =-\frac{3}{10}\) or \(z=-0.3\)