3.1 Solving Equations Algebra I.

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Presentation transcript:

3.1 Solving Equations Algebra I

Solve an equation using subtraction EXAMPLE 1 Solve an equation using subtraction Solve x + 7 = 4. x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Subtract 7 from each side. x = – 3 Simplify. CHECK Substitute – 3 for x in the original equation. x + 7 = 4 Write original equation. –3 + 7 = 4 ? Substitute –3 for x. 4 = 4 Simplify. Solution checks.

EXAMPLE 2 Solve an equation using addition Solve x – 12 = 3. x – 12 = 3 +12 x = 15

Solve an equation using division EXAMPLE 3 Solve an equation using division Solve – 6x = 48. – 6x = 48 Write original equation. – 6x – 6 48 = Divide each side by – 6. x = – 8 Simplify.

GUIDED PRACTICE for Example 2 and 3 Solve the equation. Check your solution. 1. y + 7 = 10 2. x – 5 = 3 y + 7 = 10 x – 5 = 3 +5 y + 7 – 7 = 10 – 7 y = 3 x = 8 3. q – 11 = – 5 q – 11 = – 5 +11 – 11 q = 6

GUIDED PRACTICE for Example 2 and 3 CHECK #1 CHECK #2 x – 5 = 3 y + 7 = 10 8 – 5 = 3 ? 3 + 7 = 10 ? 3 = 3 10 = 10 CHECK #3 q – 11 = –5 6 – 11 = –5 ? –5 = –5

GUIDED PRACTICE for Example 2 and 3 Solve the equation. Check your solution. 4. 6 = t – 2. 5. 4x = 48. 6 = t – 2 4x = 48 4x 4 48 = + 2 x = 12 8 = t CHECK #4 CHECK #5 4x = 48. 6 = t – 2 6 = 8 – 2 ? 4 12 = 48 ? 6 = 6 48 = 48

GUIDED PRACTICE for Example 2 and 3 Solve the equation. Check your solution. 6. – 65 = – 5y. 7. 6w = – 54. – 65 = – 5y 6w = – 54 6w 6 – 54 = – 65 – 5 – 5y = w = – 9 13 = y CHECK #6 CHECK #7 – 65 = – 5y 6w = – 54 6 – 9 = – 54 ? – 65 = – 5 ? 13 – 65 = – 65 – 54 = – 54

GUIDED PRACTICE for Example 2 and 3 Solve the equation. Check your solution. 8. 24 = – 8n. 24 = – 8n 24 – 8 – 8n = – 3 = n 24 = – 8n CHECK #8 24 = – 8 ? – 3 24 = 24

Solve an equation using multiplication EXAMPLE 4 Solve an equation using multiplication = 5 x 4 Solve SOLUTION = 5 x 4 Write original equation. 4 x = 5 Multiply each side by 4. x = 20 Simplify.

Solve the equation. Check your Solution. GUIDED PRACTICE for Example 4 Solve the equation. Check your Solution. 9. = 9 t – 3 SOLUTION = 9 t – 3 Write original equation. CHECK #9 – 3 t = 9 Multiply each side by –3. = 9. t – 3 t = –27 Simplify. = 9. – 27 – 3 ? 9 = 9

Solve the equation. Check your Solution. 10. 6 c 7 = GUIDED PRACTICE for Example 4 Solve the equation. Check your Solution. 10. 6 c 7 = SOLUTION 6 c 7 = Write original equation. = 7 c 6 Multiply each side by 7. CHECK #10 c 7 = 6 42 = c Simplify. ? = 42 7 6 6 = 6

Solve the equation. Check your Solution. 11. 13 z – 2 = GUIDED PRACTICE for Example 4 Solve the equation. Check your Solution. 11. 13 z – 2 = SOLUTION – 2 13 = z Write original equation. CHECK #11 = – 2 z 13 Multiply each side by – 2. z – 2 = 13 – 26 = z Simplify. ? = – 26 – 2 13 13 = 13

Solve the equation. Check your Solution. GUIDED PRACTICE for Example 4 Solve the equation. Check your Solution. 12. = – 11 a 5 = – 11 a 5 Write original equation. CHECK #12 5 a = – 11 Multiply each side by 5. = – 11 a 5 a = – 55 Simplify. = – 11 – 55 5 ? – 11 = – 11

Solve an equation by multiplying by a reciprocal EXAMPLE 5 Solve an equation by multiplying by a reciprocal x = 4 2 7 – Solve 7 2 – The coefficient of x is 7 2 – The reciprocal of is x = 4 2 7 – Write original equation. ( ) x ) = 2 7 – 4 Multiply each side by the 7 2 – reciprocal, x = – 14 Simplify.

Solve an equation by multiplying by a reciprocal EXAMPLE 5 Solve an equation by multiplying by a reciprocal ANSWER The solution is – 14. Check by substituting – 14 for x in the original equation. x = 4 2 7 – CHECK Write original equation. (–14) = 4 ? 2 7 – Substitute –14 for x. 4 = 4 Simplify. Solution checks.

Solve the equation. Check your Solution. w = 10 5 6 13. 6 5 GUIDED PRACTICE for Example 5 Solve the equation. Check your Solution. w = 10 5 6 13. 6 5 The coefficient of w is 5 6 The reciprocal of is w = 10 5 6 Write original equation. 5 ( ) w ) = 6 10 CHECK #13 5 Multiply each side by the 6 reciprocal, w = 10 5 6 w = 12 Simplify. (12) = 10 ? 5 6 10 = 10

Solve the equation. Check your Solution. p = 14 2 3 14. 3 2 . GUIDED PRACTICE for Example 5 Solve the equation. Check your Solution. p = 14 2 3 14. 3 2 . The coefficient of p is 2 3 is . The reciprocal of p = 14 2 3 Write original equation. 2 Multiply each side by the 3 reciprocal, 2 ( ) p ) = 3 14 CHECK #14 p = 14 2 3 p = 21 Simplify. (21) = 14 ? 2 3 14 = 14

Solve the equation. Check your Solution. GUIDED PRACTICE for Example 5 Solve the equation. Check your Solution. 15. 9 = – 3 4 m . 4 – 3 The coefficient of m is 3 – 4 – 3 4 The reciprocal of is . 9 = – 3 4 m Write original equation. CHECK #15 – 3 ( – 4 3 9 ) m ) 4 = 3 Multiply each side by the – 4 reciprocal, 9 = – 3 4 m – 12 = m 4 9 = – 3 (12) ? Simplify. 9 = 9

Solve the equation. Check your Solution. GUIDED PRACTICE for Example 5 Solve the equation. Check your Solution. 16. – 8 = – 4 5 v 5 – 4 The coefficient of v is . 4 – 5 – 4 5 The reciprocal of is . – 8 = – 4 5 v Write original equation. – 4 – ( – 5 4 8) v ) 5 = 4 Multiply each side by the – 5 reciprocal, CHECK #16 – 8 = – 4 5 v 10 = v Simplify. 5 8 = – 4 (10) ? – –8 = – 8

EXAMPLE 6 Write and solve an equation OLYMPICS In the 2004 Olympics, Shawn Crawford won the 200 meter dash. His winning time was 19.79 seconds. Find his average speed to the nearest tenth of a meter per second. SOLUTION Let r represent Crawford's speed in meters per second. Write a verbal model. Then write and solve an equation.

EXAMPLE 6 Write and solve an equation 200 = r 19.79 19.79 200 r = 10.1 r Crawford's average speed was about 10.1 meters per second. ANSWER

GUIDED PRACTICE for Example 6 17. 100 = 10.1 t 10.1t 100 10.1 = 9.9 t WHAT IF? In the example 6, suppose Shawn Crawford ran 100 meters at the same average speed he ran the 200 meters. How long would it take him to run 100 meters ? Round your answer to nearest tenth of a second. Hint: Let t represent Crawford’s time in speed. 100 = 10.1 t Therefore, about 9.9 seconds required Crawford’s to run 100 meters. 10.1t 100 10.1 = 9.9 t