Sure! Here is the detailed step-by-step solution for solving the equation [tex]\(2x + 5 = 19\)[/tex] along with matching each step to its justification:
1. Step: [tex]\(2x + 5 = 19\)[/tex]
Justification: given
2. Step: [tex]\(2x + 5 - 5 = 19 - 5\)[/tex]
Justification: subtraction property of equality
3. Step: [tex]\(2x = 14\)[/tex]
Justification: subtract
4. Step: [tex]\(2x / 2 = 14 / 2\)[/tex]
Justification: division property of equality
5. Step: [tex]\(x = 7\)[/tex]
Justification: simplify
By following these steps, we have solved the equation [tex]\(2x + 5 = 19\)[/tex] and found that [tex]\(x = 7\)[/tex].
To summarize:
- Step 1: [tex]\(2x + 5 = 19\)[/tex] (given)
- Step 2: [tex]\(2x + 5 - 5 = 19 - 5\)[/tex] (subtraction property of equality)
- Step 3: [tex]\(2x = 14\)[/tex] (subtract)
- Step 4: [tex]\(2x / 2 = 14 / 2\)[/tex] (division property of equality)
- Step 5: [tex]\(x = 7\)[/tex] (simplify)
