Sure, let's solve the equation [tex]\(2x + 5 = 19\)[/tex] step-by-step and match each step to its justification.
1. Start with the given equation:
[tex]\[
2x + 5 = 19
\][/tex]
- Justification: given
2. Apply the subtraction property of equality to isolate the term containing [tex]\(x\)[/tex]:
[tex]\[
2x + 5 - 5 = 19 - 5
\][/tex]
- Justification: subtraction property of equality
3. Simplify the equation:
[tex]\[
2x = 14
\][/tex]
- Justification: subtract
4. Apply the division property of equality to solve for [tex]\(x\)[/tex]:
[tex]\[
2x / 2 = 14 / 2
\][/tex]
- Justification: division property of equality
5. Simplify to find the value of [tex]\(x\)[/tex]:
[tex]\[
x = 7
\][/tex]
- Justification: divide
Here are all the steps with their justifications:
- [tex]\(2x + 5 = 19\)[/tex] → given
- [tex]\(2x + 5 - 5 = 19 - 5\)[/tex] → subtraction property of equality
- [tex]\(2x = 14\)[/tex] → subtract
- [tex]\(2x / 2 = 14 / 2\)[/tex] → division property of equality
- [tex]\(x = 7\)[/tex] → divide
