Sure, let's solve the equation step-by-step, matching each step to its justification:
1. Given Equation:
[tex]\[
2x + 5 = 19
\][/tex]
Justification: given
2. Subtract 5 from both sides:
[tex]\[
2x + 5 - 5 = 19 - 5
\][/tex]
Simplifying this, we get:
[tex]\[
2x = 14
\][/tex]
Justification: subtract
3. Divide both sides by 2:
[tex]\[
\frac{2x}{2} = \frac{14}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
x = 7
\][/tex]
Justification: division property of equality
So, the steps and their justifications are:
1. [tex]\(2x + 5 = 19\)[/tex] — given
2. [tex]\(2x + 5 - 5 = 19 - 5\)[/tex] — subtract
3. [tex]\(2x = 14\)[/tex]
4. [tex]\(\frac{2x}{2} = \frac{14}{2}\)[/tex] — division property of equality
5. [tex]\(x = 7\)[/tex]
Hence, the solution matches each step to its justification.
