Join the growing community of curious minds on IDNLearn.com and get the answers you need. Join our community to receive prompt, thorough responses from knowledgeable experts.
Sagot :
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].
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].
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.