algebra i 3.1 solving equations. solve an equation using subtraction example 1 solve x + 7 = 4. x +...
TRANSCRIPT
Algebra I 3.1 Solving Equations
Solve an equation using subtraction
EXAMPLE 1
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.
Solve an equation using addition
EXAMPLE 2
Solve x – 12 = 3.
x – 12 = 3
+12 +12
x = 15
Solve an equation using division
EXAMPLE 3
Solve – 6x = 48.
– 6x = 48
x = – 8
Write original equation.
– 6x– 6
48– 6= Divide each side by – 6.
Simplify.
GUIDED PRACTICE for Example 2 and 3
1. y + 7 = 10
y + 7 = 10
y + 7 – 7 = 10 – 7
y = 3
Solve the equation. Check your solution.
2. x – 5 = 3
x – 5 = 3
+5 +5
x = 8
q – 11 = – 5
q = 6
+11– 11
3. q – 11 = – 5
GUIDED PRACTICE for Example 2 and 3
CHECK #1
y + 7 = 10
3 + 7 = 10?
10 = 10
CHECK #2
CHECK #3
8 – 5 = 3?
3 = 3
x – 5 = 3
6 – 11 = –5?
–5 = –5
q – 11 = –5
GUIDED PRACTICE for Example 2 and 3
4. 6 = t – 2.
6 = t – 2
+ 2 + 2
8 = t
Solve the equation. Check your solution.
4x = 48
x = 12
4x 4
48 4=
5. 4x = 48.
CHECK #4 CHECK #5
6 = 8 – 2?
6 = 6
6 = t – 2 4x = 48.
48 = 48
4 12 = 48?
GUIDED PRACTICE for Example 2 and 3
6. – 65 = – 5y.
– 65 = – 5y
13 = y
– 65– 5
– 5y– 5=
Solve the equation. Check your solution.
6w = – 54
w = – 9
6w 6
– 54 6=
7. 6w = – 54.
– 65 = – 5y
– 65 = – 65
– 65 = – 5? 13
6w = – 54
– 54 = – 54
6 – 9 = – 54?
CHECK #6 CHECK #7
GUIDED PRACTICE for Example 2 and 3
8. 24 = – 8n.
24 = – 8n
– 3 = n
24– 8
– 8n– 8=
Solve the equation. Check your solution.
24 = – 8n
24 = 24
24 = – 8? – 3
CHECK #8
Solve an equation using multiplicationEXAMPLE 4
Write original equation.
4 x4 = 4 5 Multiply each side by 4.
x = 20 Simplify.
= 5x 4Solve
SOLUTION
= 5x4
GUIDED PRACTICE for Example 4
SOLUTION
9. = 9t– 3
= 9t– 3
Write original equation.
– 3 t– 3 = – 3 9 Multiply each side by –3.
t = –27 Simplify.
Solve the equation. Check your Solution.
9 = 9
= 9.t– 3
= 9.– 27– 3
?
CHECK #9
GUIDED PRACTICE for Example 4
SOLUTION
Write original equation.
= 7 7 c 7
6 Multiply each side by 7.
42 = c Simplify.
10. 6 c7=
6 c7=
Solve the equation. Check your Solution.
CHECK #10
6 = 6
c 7=6
?= 42 7
6
GUIDED PRACTICE for Example 4
SOLUTION
Write original equation.
= – 2 – 2 z – 2 13 Multiply each side by – 2.
– 26 = z Simplify.
11. 13 z– 2=
– 2 13 =z
Solve the equation. Check your Solution.
13 = 13
z – 2=13
?= – 26 – 2
13
CHECK #11
GUIDED PRACTICE for Example 4
12. = – 11a 5
Write original equation.
5a 5 = 5 – 11 Multiply each side by 5.
a = – 55 Simplify.
= – 11a 5
Solve the equation. Check your Solution.
– 11 = – 11
= – 11a 5
= – 11 – 555
?
CHECK #12
Solve an equation by multiplying by a reciprocal
EXAMPLE 5
Write original equation.x = 427
–
x = 427
–Solve 72–The coefficient of x is
72
–The reciprocal of27
–is
( )(x ) =27
–72
–72
– 4Multiply each side by the
72
–reciprocal,
x = – 14 Simplify.
Solve an equation by multiplying by a reciprocal
EXAMPLE 5
ANSWER
The solution is – 14. Check by substituting – 14 for x in the original equation.
CHECK Write original equation.
Substitute –14 for x.
4 = 4 Simplify. Solution checks.
x = 427
–
(–14) = 4 ?2
7–
GUIDED PRACTICE for Example 5
Solve the equation. Check your Solution.
Write original equation.
w = 105613.
5 ( )(w ) =56
6 65 10
5
Multiply each side by the 6reciprocal,
65The coefficient of w is
565
6The reciprocal of is
w = 1056
w = 12 Simplify.
10 = 10
w = 1056
(12) = 10?5
6
CHECK #13
GUIDED PRACTICE for Example 5
Solve the equation. Check your Solution.
Write original equation.
p = 142314.
2 ( )(p ) =23
3 32 14
2
Multiply each side by the 3reciprocal,
p = 1423
32
.The coefficient of p is
232
3 is .The reciprocal of
p = 21 Simplify.
14 = 14
p = 1423
(21) = 14?2
3
CHECK #14
GUIDED PRACTICE for Example 5
Solve the equation. Check your Solution.
Write original equation.
3
Multiply each side by the – 4reciprocal,
.4– 3The coefficient of m is
3– 4– 3
4The reciprocal of is .
15. 9 = – 3
4m
9 = – 3
4m
– 3(– 4
3 9 ) 3 ( m ) 4
– 4=
– 12 = m Simplify.
9 = 9
9 = – 3
4m
49 =
– 3 (12)?
CHECK #15
GUIDED PRACTICE for Example 5
Solve the equation. Check your Solution.
Write original equation.
4
Multiply each side by the – 5reciprocal,
16. – 8 = – 4
5v
– 4–(
– 54 8) 4 ( v )
5– 5
=
– 8 = – 4
5v
4– 5– 4
5The reciprocal of is .
5– 4The coefficient of v is .
10 = v Simplify.
–8 = – 8
– 8 = – 4
5v
58 =
– 4 (10)?–
CHECK #16
EXAMPLE 6 Write and solve an equation
Let r represent Crawford's speed in meters per second. Write a verbal model. Then write and solve an equation.
OLYMPICS
SOLUTION
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.
Write and solve an equation
EXAMPLE 6
Crawford's average speed was about 10.1 meters per second.
ANSWER
19.7920019.79 19.79 r=
200 = r 19.79
10.1 r
GUIDED PRACTICE for Example 6
17. 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
10.1t10010.1 10.1
=
9.9 t
Therefore, about 9.9 seconds
required Crawford’s to run
100 meters.