Download Solving Literal Equations

Solving
Equations
Solving
Literal
Equations
Solving
Absolute
Value Equations
& Inequalities
Solving
Inequalities
Word
Problems
100
100
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100
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500
Solving Equations - $100
Solve the equation.
4(6 – 3x) – (x – 8) = 3(1 – 5x)
Solving Equations - $100
4(6 – 3x) – (x – 8) = 3(1 – 5x)
24 – 12x – x + 8 = 3 – 15x
32 – 13x = 3 – 15x
2x = -29
x = -29/2 or -14½
Solving Equations - $200
Solve the equation.
3
4
4x   3x   x
10
5
Solving Equations - $200
3
4


10  4x   3x   x 
10
5


40x – 3 = 30x + 8 + 10x
40x – 3 = 40x + 8
-3 = 8
No Solution
Solving Equations - $300
Solve the equation.
x  5 3x  2 7  2x


3
4
6
Solving Equations - $300
 x  5 3x  2   7  2x 
12 


12
4   6 
 3
4(x – 5) – 3(3x + 2) = 2(7 – 2x)
4x – 20 – 9x – 6 = 14 – 4x
-5x – 26 = 14 – 4x
-x = 40
x = -40
Solving Equations - $400
Solve the equation.
2[5x + (x – 3)2] = 3x(x + 5) – x2 + 18
Solving Equations - $400
2[5x + (x – 3)2 ] = 3x(x + 5) – x2 + 18
2[5x + x2 – 6x + 9] = 3x2 + 15x – x2 + 18
2[x2 – x + 9] = 2x2 + 15x + 18
2x2 – 2x + 18 = 2x2 + 15x + 18
-17x = 0
x=0
Solving Equations - $500
Solve the equation.
12
4 1
4
 1
  4x    6x     x  
23
3 2
3
 4
Solving Equations - $500
12
4 1
4
 1
  4x    6x     x  
23
3 2
3
 4
3x 1   x 2 
1
6   2x 
     6
2 3  2 3
3
2 + 12x – 9x + 2 = 3x + 4
4 + 3x = 3x + 4
All REAL Numbers
Solving Literal Equations - $100
Solve for l.
V = lwh
Solving Literal Equations - $100
V = lwh
V =l
wh
Solving Literal Equations - $200
Solve for x.
2x + 3y = 10
Solving Literal Equations - $200
2x + 3y = 10
2x = -3y + 10
x = -3y + 10
2
or x = -3y + 5
2
Solving Literal Equations - $300
Solve for n.
L = a + (n – 1) d
Solving Literal Equations - $300
L = a + (n – 1) d
L – a = (n – 1)d
L–a=n–1
d
L – a + 1 = n OR L – a + d = n
d
d
Solving Literal Equations - $400
Solve for z.
pz – 4z = k
Solving Literal Equations - $400
pz – 4z = k
z(p – 4) = k
z=
k _
(p – 4)
Solving Literal Equations - $500
Solve for g.
rg + m = 2(g – 1)
Solving Literal Equations - $500
rg + m = 2(g – 1)
rg + m = 2g – 2
rg – 2g = -m – 2
g(r – 2) = -m – 2
g = -m – 2
r-2
Solving Absolute Value Equations & Inequalities- $100
Solve the equation.
|17 – 3x| = 43
Solving Absolute Value Equations & Inequalities- $100
|17 – 3x| = 43
17 – 3x = 43 OR 17 – 3x = -43
- 3x = 26
- 3x = -60
x = - 26/3 OR
x = 20
Solving Absolute Value Equations & Inequalities- $200
Solve the equation.
3 |4x + 5| - 6 = 42
Solving Absolute Value Equations & Inequalities- $200
3 |4x + 5| - 6 = 42
3 |4x + 5| = 48
|4x + 5| = 16
4x + 5 = 16 OR 4x + 5 = -16
4x = 11
4x = - 21
x = 11/4
OR
x = -21/4
Solving Absolute Value Equations & Inequalities- $300
Solve and graph the inequality.
|6x – 11| < 25
Solving Absolute Value Equations & Inequalities- $300
|6x – 11| < 25
Find the critical values.
|6x – 11| = 25
6x – 11 = 25
6x – 11 = -25
x=6
x = -7/3
Test values within the intervals.
x < 6 AND x > -7/3
●
●
-7/3
6
Solving Absolute Value Equations & Inequalities- $400
Solve and graph the inequality.
7 |8 – 2x| > 63
Solving Absolute Value Equations & Inequalities- $400
7 |8 – 2x| > 63
|8 – 2x| > 9
Find the critical values.
|8 – 2x| = 9
8 – 2x = 9
8 – 2x = -9
x = -1/2
x = 17/2
Test values within the intervals.
x < -1/2 OR x > 17/2
○
○
-1/2
17/2
Solving Absolute Value Equations & Inequalities- $500
Solve and graph the inequality.
½ |5x – 1| - 7 < 10
Solving Absolute Value Equations & Inequalities- $500
½ |5x – 1| - 7 < 10
½ |5x – 1| < 17
|5x – 1| < 34
Find the critical values.
|5x – 1| = 34
5x – 1 = 34
5x – 1 = -34
x=7
x = -33/5
Test values within the intervals.
x < 7 AND x > -33/5
○
○
-33/5
7
Solving Inequalities- $100
Solve and graph the inequality.
4m – 11 < 8m + 7
Solving Inequalities- $100
4m – 11 < 8m + 7
-4m < 18
( m > -4½ )
m > -9/2
●
-9/2
Solving Inequalities- $200
Solve and graph the inequality.
-3(k – 2) + 9 > 2(k – 5)
Solving Inequalities- $200
-3(k – 2) + 9 > 2(k – 5)
-3k + 6 + 9 > 2x – 10
- 3k + 15 > 2x – 10
- 5k > - 25
k<5
○
5
Solving Inequalities- $300
Solve and graph the inequality.
4 < 2y – 2 < 10
Solving Inequalities- $300
4 < 2y – 2 < 10
6 < 2y < 12
3<y<6
○
○
3
6
Solving Inequalities- $400
Solve and graph the inequality.
3n + 11 < 13 OR -3n > -12
Solving Inequalities- $400
3n + 11 < 13 OR -3n > -12
3n < 2 OR n < 4
n < 2/3 OR n < 4
n<4
○
4
Solving Inequalities- $500
Solve the and graph inequality.
3w + 8 < 2 OR w + 12 > 2 - w
Solving Inequalities- $500
3w + 8 < 2
3w < 10
w< 10/3
OR
OR
OR
w + 12 > 2 – w
2w > - 1
w > -5
All REAL Numbers
Word Problems - $100
Seven less than triple a number
is 9 more than the number.
Find the number.
Word Problems - $100
3x – 7 = 9 + x
x=8
the number is 8
Word Problems - $200
Find 3 consecutive integers such that
the difference of the squares of the
last and first is equal to the product
of 5 and the second integer.
Word Problems - $200
(x + 2)2 – x2 = 5(x + 1)
x2 + 4x + 4 – x2 = 5x + 5
4x + 4 = 5x + 5
-x = 1
x = -1
x = -1, x + 1 = 0, and x + 2 = 1
Word Problems - $300
The perimeter of a rectangular park
is 624 yards. If the length is 8 yards
more than 3 times the width, find
the dimensions of the park.
Word Problems - $300
2w + 2(3w + 8) = 624
2w + 6w + 16 = 624
8w + 16 = 624
8w = 608
w = 76 yards
3w + 8 = 236 yards
park is 76 yards x 236 yards
Word Problems - $400
Jim and Joe started on trips from
San Francisco traveling in opposite
directions. Jim traveled 15 km/h
faster than Joe. After 4 hours, they
were 420 km apart. How fast was
each person traveling?
Word Problems - $400
4x + 4(15 + x) = 420
4x + 60 + 4x = 420
8x + 60 = 420
8x = 360
x = 45 km/h
15 + k = 60 km/h
Joe – 45 km/h
Jim – 60 km/h
Word Problems - $500
A coin bank contains twice as many
nickels as quarters, three times as many
pennies as quarters, and no dimes. If the
bank contains $7. 60, how many of each
coin does it contain?
Word Problems - $500
2x(.05) + x(.25) + 3x(.01) = 7.60
0.1x + .25x + .03x = 7.60
0.38x = 7.60
x = 20
20 quarters, 40 nickels, and
60 pennies