Joseph used the problem-solving strategy Work Backward to solve the inequality 2n+5<13. Shawnee solved the inequality using the algebraic method. Compare the two methods.
THANK YOU!
2n + 5 < 13
2n < 13-5
2n < 8
n < 4
any other method only complicates and confuses the problem.
I have no idea what this "problem-solving strategy Work Backward" is.
Both Joseph and Shawnee used different methods to solve the inequality 2n+5<13. Joseph used the problem-solving strategy known as Work Backward, while Shawnee used the algebraic method.
To understand and compare the two methods, let's go through each step for both Joseph's Work Backward method and Shawnee's algebraic method.
1. Joseph's Work Backward method:
- Joseph started by considering the given inequality: 2n+5<13.
- He then looked for the final step or condition that would make the inequality true.
- In this case, he realized that if he subtracted 5 from both sides, he would end up with 2n<8, which is a simpler inequality.
- Finally, by dividing both sides of this new inequality by 2, he found the solution: n<4.
2. Shawnee's algebraic method:
- Shawnee started with the same given inequality: 2n+5<13.
- She began by isolating the variable on one side of the inequality.
- To do this, she subtracted 5 from both sides, resulting in 2n<8.
- Next, she divided both sides of the inequality by 2 to solve for n and obtain n<4.
- Shawnee's method followed the standard algebraic approach to solving inequalities, which involves isolating the variable and applying inverse operations.
Comparing the two methods:
- Joseph's Work Backward method focused on identifying the final step that directly leads to the solution. In this case, he worked backward by solving the inequality step-by-step in reverse order.
- Shawnee's algebraic method utilized standard algebraic procedures to isolate the variable and simplify the inequality step-by-step.
- Both methods led to the same solution, n<4, which means that any value of n less than 4 will satisfy the original inequality.
- While Joseph's Work Backward method can provide an alternative approach to problem-solving, the algebraic method is more widely used and applicable to a broader range of mathematical equations and inequalities.
In conclusion, Joseph's Work Backward method and Shawnee's algebraic method are two distinct approaches to solving the inequality 2n+5<13. Both methods yield the same solution, but the algebraic method is generally more widely used in mathematics.