Objectives Vocabulary Example 1 Example 2 Example 3
Objectives Vocabulary Example 1 Example 2 Example 3 Example 4 Quick Quiz
• To solve equations without using the balance puzzle model • To express a balance puzzle as an algebraic equation • To represent an equation as a balance puzzle • To solve simple word problems by writing and solving equations
• inequality • solution set
Solve x + 4 = 5. Method 1 Use models. Model the equation. Solving Equations Using Algebra Tiles Remove 4 counters from each side.
Method 2 Use symbols. x+4= 5 – 4=– 4 x= 1 Write the equation. Subtract 4 from each side to “undo” the addition of 4 on the left. 5– 4=1 Answer: The solution is 1. Check 1+4=5
Solve x + 7 = 13. A. x = – 20 B. x = – 6 C. x = 6 D. x = 20 1. 2. 3. 4. A B C D
PENNSYLVANIA The width of Pennsylvania (from north to south) is 280 miles. This is 120 miles more than the length of the state (from east to west). Write and solve an addition equation to find the length of Pennsylvania. Words length plus 120 miles is 280 miles Variable Let x represent the length of Pennsylvania. Equation x + 120 = 280
x + 120 = 280 – 120 = – 120 x = 160 Write the equation. Subtract 120 from each side. 280 – 120 = 160 Answer: So, the length of Pennsylvania is 160 miles.
INTERNET Steve was on the Internet for 40 minutes last night. This was 15 more minutes than Beth spent on the Internet the same night. Write and solve an addition equation to find the amount of time Beth spent on the Internet last night. A. 15 – t = 40; 20 minutes B. 15 + t = 40; 25 minutes C. 40 + t = 15; 25 minutes D. 40 – t = 15; 55 minutes 1. 2. 3. 4. A B C D
Solve x – 5 = – 1. Check your solution. x – 5 = – 1 Write the equation. +5=+ 5 Add 5 to each side. x = 4 Simplify. Check x – 5 = – 1 ? 4 – 5 = – 1 Answer: The solution is 4.
Solve d – 8 = – 5. Check your solution. A. – 13 B. – 3 C. 3 D. 13 1. 2. 3. 4. A B C D
For the given value, state whether the inequality is true or false. x – 4 < 6; x = 0 x– 4<6 ? 0– 4<6 – 4 < 6 Write the inequality. Replace x with 0. Simplify Answer: Since – 4 is less than 6, – 4 < 6 is true.
For the given value, state whether the inequality is true or false. x – 5 < 8; x = 16 A. true B. false 1. 2. A B
In a balance puzzle, 4 bags and 2 blocks balance 2 bags and 10 blocks. Select the equation describing the balance. A. 4 b + 2 = 2 b + 10 B. 4 + 2 = 2 b + 10 C. 4 b + 2 = 4 + 10 D. 6 b = 12 1. 2. 3. 4. A B C D
Solve the inequality 3 s – 2 > 19 by doing the same thing to both sides. A. s > 8. 3 B. s > 7 C. s > 5. 6 D. s > 8 1. 2. 3. 4. A B C D
A. Amelia is selecting a new printer for the school newspaper staff. Printer A costs $500. It costs $0. 07 for each page printed. Printer B costs $800. It costs $0. 05 for each page printed. Write an equation you could solve to find the number of pages at which the total cost for each printer is the same. The total cost of the printer is the purchase cost and the cost to print each page. A. 500 + 0. 07 = 800 + 0. 05 B. 500 + 0. 07 x = 800 + 0. 05 C. 500 + 0. 07 x = 800 + 0. 05 x D. 500 x + 0. 07 = 800 x + 0. 05 1. 2. 3. 4. A B C D
B. Amelia is selecting a new printer for the school newspaper staff. Printer A costs $500. It costs $0. 07 for each page printed. Printer B costs $800. It costs $0. 05 for each page printed. Solve the equation in 3 A by doing the same thing to both sides. A. x = 4, 000 B. x = 40, 000 C. x = 13, 000 D. x = 15, 000 1. 2. 3. 4. A B C D
A. B. C. 3 D. 2 1. 2. 3. 4. A B C D
Image Bank Math Tools Multilingual e-Glossary Solving Equations Using Algebra Tiles Spreadsheets Solving Equations Two-Step Equations
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