Solve Equations
infinite, one, or none?
multiply polynomial
factor polynomial
100
38=2a+54
38-54=2a -16=2a -8=a
100
Is this equation an identity (infinite solutions) or is there no solution? 8(h - 1)=6h+4+2h
8h-1=8h+4 8h =8h+5 not true NO SOLUTION
100
–3x(4x2 – x + 10)
= –3x(4x2) – 3x(–x) – 3x(10) = –12x3 + 3x2 – 30x
100
9x 2 + 3x - 2
(3x + 2)(3x - 1)
200
t + 18.1 = 23.9
t=23.9-18.1 t=5.8
200
Is this equation an identity (infinite solutions), is there just one solution, or is there no solution? c+3 ------- = 15 5
Multiply both sides by 5 to cancel out denominator... c+3 = 75 c = 75 -3 c= 72 ONE SOLUTION
200
(x + 3)(x + 2)
= (x + 3)(x) + (x + 3)(2) = x(x) + 3(x) + x(2) + 3(2) = x2 + 3x + 2x + 6 = x2 + 5x + 6
200
x 3 + 2x 2 - 16x - 32
(x 3 + 2x 2) - (16x + 32)
300
18.9 = 2.1x
18.9 divided by 2.1 = x x = 9
300
Is this equation an identity (infinite solutions), is there just one solution, or is there no solution? 4c-10=2(2c-5)
4c-10=4c-10 Both sides exactly the same...IDENTITY (infinite solutions)
300
(x + 3)(x + 2)
x2 + 5x + 6
300
(x + 1) 2 - 4
(x - 1)(x + 3)
400
1/2 (b-3) = 5/2 Read: one half (b - 3) = five halves
distribute: 1/2b - 1/2(3) = 5/2 multiply: 1/2b - 3/2 = 5/2 junk: 1/2b = 5/2 + 3/2 1/2b = 8/2, simplifies to 1/2b=4 divide: b = 8
400
Is this equation an identity (infinite solutions), is there just one solution, or is there no solution? 5+4p=2(2p+1)
5+4p = 4p + 2 5-2 + 4p = 4p 3+4p = 4p Sides don't match, no solution is possible. NO SOLUTION
400
(4x2 – 4x – 7)(x + 3)
= (4x2 – 4x – 7)(x) + (4x2 – 4x – 7)(3) = 4x2(x) – 4x(x) – 7(x) + 4x2(3) – 4x(3) – 7(3) = 4x3 – 4x2 – 7x + 12x2 – 12x – 21 = 4x3 – 4x2 + 12x2 – 7x – 12x – 21 = 4x3 + 8x2 – 19x – 21
400
x 2 + 5x + 6
(x + 2)(x + 3)
500
9p + 6 - 3p = 45
combine like terms: 6p + 6 = 45 junk: 6p = 45-6 6p = 39 divide: p= 6.5
500
Is this equation an identity (infinite solutions), is there just one solution, or is there no solution? 3x - 3 = x + 7
Get x's on one side... 3x- x -3 = 7 Combine like terms... 2x -3 = 7 Junk........................ 2x = 7 + 3 OR 2x=10 Divide...................... x = 5
500
(x + 2)(x3 + 3x2 + 4x – 17)
x4 + 5x3 + 10x2 – 9x – 34
500
x 3 - 1
(x - 1)(x 2 + x + 1)
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