Let's analyze the steps Kira took to solve the equation step-by-step and identify the properties of equality that were used.
1. Original equation:
[tex]\[
\frac{7}{2} - 2x = \frac{11}{2}
\][/tex]
2. Subtract [tex]\(\frac{7}{2}\)[/tex] from both sides to isolate the term with the variable [tex]\(x\)[/tex]:
[tex]\[
\frac{7}{2} - \frac{7}{2} - 2x = \frac{11}{2} - \frac{7}{2}
\][/tex]
[tex]\[
-2x = \frac{4}{2}
\][/tex]
In this step, Kira used the Subtraction Property of Equality to combine the constant terms. This property states that if you subtract the same value from both sides of an equation, the equation remains balanced.
3. Simplify the right-hand side:
[tex]\[
-2x = 2
\][/tex]
4. Divide both sides by [tex]\(-2\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[
-2x \div (-2) = 2 \div (-2)
\][/tex]
[tex]\[
x = -1
\][/tex]
In this step, Kira used the Division Property of Equality to isolate the variable. This property states that if you divide both sides of an equation by the same non-zero value, the equation remains balanced.
So, to summarize:
- The first step is to use the Subtraction Property of Equality to combine the constant terms.
- The second step is to use the Division Property of Equality to isolate the variable.
