Certainly! Let's solve the equation step by step and match each step to its justification.
Problem: Solve the equation [tex]\(2x + 5 = 19\)[/tex].
Step-by-Step Solution:
1. Given:
[tex]\[
2x + 5 = 19
\][/tex]
This is the equation we start with.
2. Subtraction Property of Equality:
[tex]\[
2x + 5 - 5 = 19 - 5
\][/tex]
We subtract 5 from both sides of the equation to start isolating the variable [tex]\(x\)[/tex].
3. Subtract:
[tex]\[
2x = 14
\][/tex]
After subtracting 5 from both sides, we simplify to [tex]\(2x = 14\)[/tex].
4. Division Property of Equality:
[tex]\[
x = \frac{14}{2}
\][/tex]
We divide both sides of the equation by 2 to solve for [tex]\(x\)[/tex].
5. Divide:
[tex]\[
x = 7
\][/tex]
Dividing 14 by 2, we get [tex]\(x = 7\)[/tex].
Summary:
- [tex]\(2x + 5 = 19\)[/tex] (given)
- [tex]\(2x + 5 - 5 = 19 - 5\)[/tex] (subtraction property of equality)
- [tex]\(2x = 14\)[/tex] (subtract)
- [tex]\(x = \frac{14}{2}\)[/tex] (division property of equality)
- [tex]\(x = 7\)[/tex] (divide)
Thus, the final solution to the equation [tex]\(2x + 5 = 19\)[/tex] is [tex]\(x = 7\)[/tex].
