QuestionGet Ready!
See Lesson 1-3
Ordering Rational Numbers
Complete each statement with , or .
1. -3 ■ -5
2.
3.
4.
See Lesson 1-5 Absolute Value
Simplify each expression.
5.
6.
7.
See Lesson 2-1 Solving One-Step Equations
Solve each equation. Check your solution.
8.
9.
10.
11.
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13.
14.
15.
see Lesson 2-2 Solving Two-Step Equations
Solve each equation. Check your solution.
16.
17.
18.
19.
20.
21.
22.
23.
24.
See Lessons
2-3 and 2-4
Solving Multi-Step Equations
Solve each equation. Check your solution.
25.
26.
28.
29.
27.
30.
Looking Ahead Vocabulary
31. You make a compound word, such as houseboat, by joining two words together. Why do you think is called a compound inequality?
32. The intersection of two roads is the place where the roads cross. How would you define the intersection of two groups of objects?
Studdy Solution
STEP 1
1. The problem involves ordering rational numbers, simplifying expressions, solving one-step, two-step, and multi-step equations, and understanding vocabulary related to compound inequalities and intersections.
2. Rational numbers include integers, fractions, and decimals.
3. Absolute value represents the distance from zero on the number line.
4. Equations need to be solved for the variable, and solutions should be checked for accuracy.
5. Compound inequalities involve two inequalities joined by "and" or "or".
6. The intersection of two groups refers to elements common to both groups.
STEP 2
1. Order rational numbers using comparison symbols.
2. Simplify expressions involving absolute values.
3. Solve one-step equations and check solutions.
4. Solve two-step equations and check solutions.
5. Solve multi-step equations and check solutions.
6. Understand vocabulary related to compound inequalities and intersections.
STEP 3
Order rational numbers using comparison symbols.
1. Compare and : Since is greater than , the symbol is .
2. Compare and : Since , the symbol is .
3. Compare and : Since is greater than , the symbol is .
4. Compare and : Since , the symbol is .
STEP 4
Simplify expressions involving absolute values.
5. : Calculate the absolute value , so the expression becomes .
6. : Calculate the absolute value , so the expression becomes .
7. : Calculate the absolute value , so the expression becomes .
STEP 5
Solve one-step equations and check solutions.
8. : Add 4 to both sides to get .
9. : Subtract 4 from both sides to get .
10. : Multiply both sides by to get .
11. : Multiply both sides by 12 to get .
12. : Add 8 to both sides to get .
13. : Add 7 to both sides to get .
14. : Multiply both sides by to get .
15. : Multiply both sides by to get .
STEP 6
Solve two-step equations and check solutions.
16. : Add 5 to both sides to get , then multiply by 4 to get .
17. : Subtract 4 from both sides to get , then divide by 4.2 to get .
18. : Subtract 6 from both sides to get , then multiply by to get .
19. : Add 4 to both sides to get , then multiply by to get .
20. : Subtract 2.3 from both sides to get , then divide by 4 to get .
21. : Add 7 to both sides to get , then multiply by to get .
22. : Subtract 1.3 from both sides to get , then divide by 3 to get .
23. : Add 3.7 to both sides to get , then divide by 5.3 to get .
24. : Subtract 5 from both sides to get , then multiply by to get .
STEP 7
Solve multi-step equations and check solutions.
25. : Combine like terms to get , subtract 7 to get , then divide by 10 to get .
26. : Subtract from both sides to get , add 16 to get , then divide by 7 to get .
27. : Simplify to , then subtract from both sides to get , multiply by 3/2 to get .
28. : Distribute to get , add to both sides to get , add 12 to get , then divide by 8 to get .
29. : Distribute to get , combine like terms to get , add 6 to get , then divide by 4 to get .
30. : Subtract from both sides to get , add 5 to get , then multiply by 3 to get .
STEP 8
Understand vocabulary related to compound inequalities and intersections.
31. A compound inequality like is called a compound inequality because it combines two inequalities, and , into one statement that describes a range of values for .
32. The intersection of two groups of objects is the set of elements that are common to both groups.
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