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 \(c = 3\).

$$
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$$

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.

$$
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$$

Step3: Subtract 13 from both sides

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

$$
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$$

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 \(z=-0.3\)