Question

given: $overline{pd}congoverline{da}$
$pd = 9x - 7$ and $da = 38$
prove: $x = 5$

statements	reasons
2. $pd = 9x - 7$ and $da = 38$	2. given
3. $9x - 7=38$	3. definition of congruent
4.	4. transitive property of equality
5. $9x = 45$	5.
6.	6.

Explanation:

Step1: Substitute given values

Since $\overline{PD}\cong\overline{DA}$, then $PD = DA$. Substituting $PD=9x - 7$ and $DA = 38$, we get the equation $9x-7=38$.

Step2: Add 7 to both sides

To isolate the term with $x$, we use the addition - property of equality. Adding 7 to both sides of the equation $9x-7 = 38$ gives $9x-7 + 7=38 + 7$, which simplifies to $9x=45$.

Step3: Divide both sides by 9

Using the division - property of equality, we divide both sides of the equation $9x = 45$ by 9. So, $\frac{9x}{9}=\frac{45}{9}$, and $x = 5$.

Answer:

1. $\overline{PD}\cong\overline{DA}$ - Given
2. $PD = 9x - 7$ and $DA = 38$ - Given
3. $9x-7 = 38$ - Definition of Congruent
4. $9x-7+7 = 38 + 7$ - Addition Property of Equality
5. $9x=45$ - Simplification
6. $x = 5$ - Division Property of Equality