Sure, let's go through the steps of solving the given equation and the corresponding mathematical properties used at each step.
Given the equation:
[tex]\(\frac{5}{c} x + 7 = 22\)[/tex]
Step 1: Subtracting 7 from both sides (Subtraction Property of Equality)
To isolate the term with the variable, we first need to get rid of the constant on the left-hand side.
Subtract 7 from both sides:
[tex]\[
\frac{5}{c} x + 7 - 7 = 22 - 7
\][/tex]
This simplifies to:
[tex]\[
\frac{5}{c} x = 15
\][/tex]
Reason: Subtraction Property of Equality
Step 2: Multiply both sides by c (Multiplication Property of Equality)
Next, to eliminate the fraction, multiply both sides of the equation by [tex]\(c\)[/tex]:
[tex]\[
c \left(\frac{5}{c} x\right) = 15c
\][/tex]
This simplifies to:
[tex]\[
5x = 15c
\][/tex]
Reason: Multiplication Property of Equality
Step 3: Divide both sides by 5 (Division Property of Equality)
Finally, to solve for [tex]\(x\)[/tex], divide both sides of the equation by 5:
[tex]\[
\frac{5x}{5} = \frac{15c}{5}
\][/tex]
This simplifies to:
[tex]\[
x = 3c
\][/tex]
Reason: Division Property of Equality
Put together, we have transformed the initial equation by isolating [tex]\(x\)[/tex] step by step using the properties of equality. Here are the final pairs showing statements and explanations:
Pairs: Statements:
1. [tex]\(\frac{5}{c} x + 7 = 22\)[/tex] — (Given)
2. [tex]\(\frac{5}{c} x = 15\)[/tex] — (Subtraction Property of Equality)
3. [tex]\(5x = 15c\)[/tex] — (Multiplication Property of Equality)
4. [tex]\(x = 3c\)[/tex] — (Division Property of Equality)
