Unit 5 One- & Two-Step Equations LESSON 10 One- & Two-Step Equations Review Practice Answers
1. -41
2.x+1.5=0.75
3.n − 15.50 = 34.63 ; the original cost of the groceries Nick bought was $50.13
4.c + 40.99 = 50 ; Mela receives $9.01 in change
5. 16x=64
6.-2x=11/2
7.c/1.95=5
8. 4 hours
9. She did not divide both sides by -1
10. He incorrectly added -1/8 and 5/2
11. Gabriel bought a new pair of shoes for $29
12. You need to complete 15 math lessons. If you complete 412 math lessons today and 312 lessons per day after that, you can complete the lessons in 3 more days.
13. 11
14. 7
15. Subtraction and Division
Unit 5 One- & Two-Step Equations LESSON 10 One- & Two-Step Equations Review Practice Answers
1. -41
2.x+1.5=0.75
3.n − 15.50 = 34.63 ; the original cost of the groceries Nick bought was $50.13
4.c + 40.99 = 50 ; Mela receives $9.01 in change
5. 16x=64
6.-2x=11/2
7.c/1.95=5
8. 4 hours
9. She did not divide both sides by -1
10. He incorrectly added -1/8 and 5/2
11. Gabriel bought a new pair of shoes for $29
12. You need to complete 15 math lessons. If you complete 412 math lessons today and 312 lessons per day after that, you can complete the lessons in 3 more days.
13. 11
14. 7
15. Subtraction and Division
16. Addition and Multiplication
17. 10.5
18. x = 6
19. x = 25
20. y = -8
21. m = 16.25
22. n = 45
23. x = -7
24. m = 13
25. x = 4
Here are step-by-step solutions to the given problems:
1. To solve this one-step equation, we need to isolate the variable x.
Add 41 to both sides of the equation: x + 41 - 41 = -41 + 41.
Simplify both sides to get: x = -41.
Therefore, the solution to the equation is x = -41.
2. To solve this two-step equation, we need to isolate the variable x.
Subtract 1.5 from both sides of the equation: x + 1.5 - 1.5 = 0.75 - 1.5.
Simplify both sides to get: x = -0.75.
Therefore, the solution to the equation is x = -0.75.
3. To solve this two-step equation, we need to isolate the variable n.
Add 15.50 to both sides of the equation: n - 15.50 + 15.50 = 34.63 + 15.50.
Simplify both sides to get: n = 50.13.
Therefore, the solution to the equation is n = 50.13.
4. To solve this two-step equation, we need to isolate the variable c.
Subtract 40.99 from both sides of the equation: c + 40.99 - 40.99 = 50 - 40.99.
Simplify both sides to get: c = 9.01.
Therefore, the solution to the equation is c = 9.01.
5. To solve this one-step equation, we need to isolate the variable x.
Divide both sides of the equation by 16: 16x/16 = 64/16.
Simplify both sides to get: x = 4.
Therefore, the solution to the equation is x = 4.
6. To solve this one-step equation, we need to isolate the variable x.
Divide both sides of the equation by -2: -2x/-2 = (11/2)/-2.
Simplify both sides to get: x = -11/4.
Therefore, the solution to the equation is x = -11/4.
7. To solve this one-step equation, we need to isolate the variable c.
Divide both sides of the equation by 1.95: c/1.95 = 5/1.95.
Simplify both sides to get: c = 9.75.
Therefore, the solution to the equation is c = 9.75.
8. There is no equation provided for this problem, so we cannot determine an exact solution. However, 4 hours is a possible answer to a problem asking for the solution to an equation.
9. This is not a question but a statement. It seems to be describing an error made by someone while solving an equation.
10. This is not a question but a statement. It seems to be describing an error made by someone while solving an equation.
11. This is not a question but a statement. It provides information about Gabriel's purchase.
12. To solve this word problem, we need to determine the number of days it takes to complete the lessons.
Let's set up an equation: 412 + 312x = 15, where x represents the number of days after today.
Subtract 412 from both sides of the equation: 412 - 412 + 312x = 15 - 412.
Simplify both sides to get: 312x = -397.
Divide both sides of the equation by 312: x = -397/312.
Therefore, it will take approximately 3 more days to complete the lessons.
13. This is not a question but a statement. It provides the answer to an unknown problem.
14. This is not a question but a statement. It provides the answer to an unknown problem.
15. This is not a question but a statement. It describes the operations involved in two-step equations. Subtract and division are the operations used in these equations.
I apologize for the error in the previous response. Here are the correct step-by-step solutions to the given problems:
9. She did not divide both sides by -1: To solve the equation, she should divide both sides by the same non-zero number.
10. He incorrectly added -1/8 and 5/2: To add fractions with different denominators, you need to find a common denominator. The correct step would be to find a common denominator and then add the fractions.
If you have any further questions or need clarification on any specific problem, please let me know.
To get the answers to these equations, you need to follow the steps to solve one- and two-step equations.
1. - To solve one-step equations, perform inverse operations to isolate the variable. In this case, the equation is already solved, and the answer is -41.
2. x + 1.5 = 0.75 - To isolate the variable x, subtract 1.5 from both sides of the equation. This gives you x = -0.75.
3. n - 15.50 = 34.63 - To isolate the variable n, add 15.50 to both sides of the equation. This gives you n = 50.13.
4. c + 40.99 = 50 - To isolate the variable c, subtract 40.99 from both sides of the equation. This gives you c = 9.01.
5. 16x = 64 - To isolate the variable x, divide both sides of the equation by 16. This gives you x = 4.
6. -2x = 11/2 - To isolate the variable x, divide both sides of the equation by -2. This gives you x = -11/4 or -2.75.
7. c/1.95 = 5 - To isolate the variable c, multiply both sides of the equation by 1.95. This gives you c = 9.75.
8. 4 hours - This answer doesn't have an equation to solve. It is a direct answer.
9. She did not divide both sides by -1 - This answer doesn't have an equation to solve. It is explaining a mistake made by someone in solving an equation.
10. He incorrectly added -1/8 and 5/2 - This answer doesn't have an equation to solve. It is explaining a mistake made in arithmetic.
11. Gabriel bought a new pair of shoes for $29 - This answer doesn't have an equation to solve. It is a direct answer to a question.
12. You need to complete 15 math lessons. If you complete 412 math lessons today and 312 lessons per day after that, you can complete the lessons in 3 more days - This answer doesn't have an equation to solve. It is providing a calculation based on the given information.
13. 11 - This answer doesn't have an equation to solve. It is a direct answer to a question.
14. 7 - This answer doesn't have an equation to solve. It is a direct answer to a question.
15. Subtraction and Division - This answer doesn't have an equation to solve. It is describing the operations involved in the equations.