Equations with Variables on Both Sides ALGEBRA 1
Equations with Variables on Both Sides ALGEBRA 1 LESSON 2 -2 (For help, go to Lessons 1 -7 and 2 -3. ) Simplify. 1. 6 x – 2 x 2. 2 x – 6 x 3. 5 x – 5 x 4. – 5 x + 5 x Solve each equation. 5. 4 x + 3 = – 5 6. –x + 7 = 12 7. 2 t – 8 t + 1 = 43 8. 0 = – 7 n + 4 – 5 n 2 -2
Equations with Variables on Both Sides ALGEBRA 1 LESSON 2 -2 Solutions 1. 6 x – 2 x = (6 – 2)x = 4 x 2. 3. 5 x – 5 x = (5 – 5)x = 0 4. – 5 x + 5 x = (– 5 + 5)x = 0 5. 4 x + 3 = – 5 4 x = – 8 x = – 2 7. 2 t – 8 t + 1 = – 6 t = t= 6. 43 43 42 – 7 8. 2 -2 2 x – 6 x = (2 – 6)x = – 4 x –x + 7 = 12 –x = 5 x = – 5 0 0 12 n n = = – 7 n + 4 – 5 n – 12 n + 4 4 1 3
Equations with Variables on Both Sides ALGEBRA 1 LESSON 2 -2 Solve each equation. a. – 6 z + 8 = z + 10 – 7 z – 6 z + 8 = – 6 z + 10 Combine like terms. – 6 z + 8 + 6 z = – 6 z + 10 + 6 z Add 6 z to each side. 8 = 10 Not true for any value of z! This equation has no solution b. 4 – 4 y = – 2(2 y – 2) 4 – 4 y = – 4 y + 4 Use the Distributive Property. 4 – 4 y + 4 y = – 4 y + 4 y Add 4 y to each side. 4 = 4 Always true! The equation is true for every value of y, so the equation is an identity. 2 -2
Equations with Variables on Both Sides ALGEBRA 1 LESSON 2 -2 Solve each equation. 1 1. 3 – 2 t = 7 t + 4 – 9 2. 4 n = 2(n + 1) + 3(n – 1) 1 3. 3(1 – 2 x) = 4 – 6 x no solution 4. You work for a delivery service. With Plan A, you can earn $5 per hour plus $. 75 per delivery. With Plan B, you can earn $7 per hour plus $. 25 per delivery. How many deliveries must you make per hour with Plan A to earn as much as with Plan B? 4 deliveries 2 -2
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