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What are the three types of solutions we can have when solving an equation?
1 solution, no solutions, or infinite solutions
Solving Equations
2x - 1 = 7
x = 4
Solve: I=Prt for t
I/pr = t
How many solutions can you have when solving absolute value equations? List all possibilities!!!
Two or None
4 = -8 + x
x= 12
How is the first step for solving each of these equations different? Be specific!
x/2 + 3 = 9
(x + 3)/2 = 9
One you have to subtract 3 from both sides first, the other you need to multiply both sides by 2 first.
Solving Equations
4(6 + 5x) = 124
x = 5
Solve Ax + By = C for y
y= C-Ax/B
How can you tell if an absolute value equation will have no solution? Be specific and use a complete sentence!
The equation equals a negative number when the brackets are by themselves.
x + 12 = 0
x= -12
Jerry says "To solve -5x = 15 you would add 5 to both sides of the equation." Explain Jerry's mistake. Be specific!
He said you should add but you divide both sides of the equation by -5.
Solving Equations
6(6n - 2) = 8n - 40
n = -1
g = b - ca
solve for a
a = (b-g)/c or a = (g-b)/(-c)
solve for a
|8m-8| = 40
m = {-4, 6}
3x=0
x= 0
Solving for x
1/4x + x = -3 + 1/2x
x = -4
Solving Equations
5x + 5 + 4x = 4 + 9x + 6
no solution
Solve for x
y = (x + z)/w
x = yw - z
-5|4p+4| = -40
p = {-3, 1}
5x = -80
x= -16
Write an equation to model the word problem:
The sum of three consecutive integers is 84. Let x represent the smallest of the three numbers. (You don't have to find the three numbers!)
x + x + 1 + x + 2 = 84
Solving Equations
-5(8n - 4) - n = 20 - 41n
infinite solutions
What are literal equations? Give an example.
Equations with multiple variables.
2|g-5|+7 = 13
g = {2, 8}
16 = x/2
x= 32