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Solve each equation and justify each step by using the Properties of Equality. Show all your work.

1. [tex]9 - 2c = -13[/tex]

\begin{tabular}{|l|l|}
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STEPS & JUSTIFICATION \\
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Subtract 9 from both sides: [tex]9 - 2c - 9 = -13 - 9[/tex] & Subtraction Property of Equality \\
\hline
Simplify: [tex]-2c = -22[/tex] & Simplification \\
\hline
Divide both sides by -2: [tex]\frac{-2c}{-2} = \frac{-22}{-2}[/tex] & Division Property of Equality \\
\hline
Simplify: [tex]c = 11[/tex] & Simplification \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To solve the equation [tex]\(9 - 2c = -13\)[/tex], we will use the Properties of Equality and show each step in detail.

### Step-by-Step Solution:

#### 1. Start with the initial equation:
[tex]\[ 9 - 2c = -13 \][/tex]

#### 2. Subtract 9 from both sides of the equation:
[tex]\[ (9 - 2c) - 9 = -13 - 9 \][/tex]

Justification: Subtraction Property of Equality
Subtracting the same number from both sides of an equation keeps the equation balanced.

Simplifying this step:
[tex]\[ -2c = -22 \][/tex]

#### 3. Divide both sides of the equation by -2:
[tex]\[ \frac{-2c}{-2} = \frac{-22}{-2} \][/tex]

Justification: Division Property of Equality
Dividing both sides of an equation by the same nonzero number keeps the equation balanced.

Simplifying this step:
[tex]\[ c = 11 \][/tex]

### Final Answer:
[tex]\[ c = 11 \][/tex]

This is the solution to the equation [tex]\(9 - 2c = -13\)[/tex].
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