It appears that there is some confusion in the layout of the equations and operations. Let's break down and correct them step-by-step, ensuring that each step includes a clear justification along the way.
Assume we want to solve for [tex]\(x\)[/tex] in the initial equation [tex]\(2x + 5 = 19\)[/tex].
1. Given:
[tex]\[
2x + 5 = 19
\][/tex]
2. Subtraction property of equality:
To isolate the term [tex]\(2x\)[/tex], we subtract 5 from both sides of the equation.
[tex]\[
2x + 5 - 5 = 19 - 5
\][/tex]
Simplifying, we get:
[tex]\[
2x = 14
\][/tex]
3. Division property of equality:
To solve for [tex]\(x\)[/tex], divide both sides by 2.
[tex]\[
\frac{2x}{2} = \frac{14}{2}
\][/tex]
Simplifying, we get:
[tex]\[
x = 7
\][/tex]
Therefore, the solution to the equation [tex]\(2x + 5 = 19\)[/tex] is [tex]\(x = 7\)[/tex]. Matching each step to its justification:
- [tex]\(\boxed{2x + 5 = 19}\)[/tex] - Given
- [tex]\(\boxed{2x + 5 - 5 = 19 - 5}\)[/tex] - Subtraction property of equality
- [tex]\(\boxed{2x = 14}\)[/tex] - Simplified after applying the subtraction property
- [tex]\(\boxed{\frac{2x}{2} = \frac{14}{2}}\)[/tex] - Division property of equality
- [tex]\(\boxed{x = 7}\)[/tex] - Simplified after applying the division property
Thus, each step can be clearly understood and justified within the problem-solving process for linear equations.
