Solving Equations
x + b = c
x = c - b
5x - 2 = 5x + 4
-2 = 4 is not true!
No solution
x > 3
Plot it on a number line
Interval Notation
(3, infinity)
We will graph it on the board since the program doesn't allow picture or symbols.
Yoni has 12 dollars less than Levi. If Levi spends half of his money, and Yoni spends none, then Yoni will have two dollars more than Levi. How much money did they both start with?
Let Y = The amount of money Yoni has to start with.
Let L = The amount of money Levi has to start with.
Y = L - 12
Y = ½ L + 2
½ L + 2 = L - 12
x = 5
ax - b = c
x = (c - b)/a
2x + 3 = 5
x = 1
It does have a solution. It has 1 solution!
Plot it on a number line
Interval notation
x < 5
(-infinity, 5)
We will draw the number line on the board
Write an equation and solve for n. *hint use let statements.
The sum of 3 less than 5 times a number and the number increased by 9 is 24. What is the number?
Let n = a number
(5n - 3) + (n + 9) = 24
n = 3
The number is 3
3(x + 2) = 2x + 10
x = 4
x = c/(a-b)
5(2x + 6) = 10x + 2
30 = 2 is not true!
It has no solutions!
x <= 5 and x > 2
Plot it on a number line
Write it as a singular Inequality
Write it in interval notation
Single Inequality: 2< x <= 5
Interval Notation: (2, 5]
We will draw the number line on the board
Noam is 43 years old and his daughter Batya is 7. In n-years Noam will be four times as old as Batya is at that point. Set up and solve an equation for n. Then state both Noam and Batya's ages after n-years.
Noam's age in n years = 43 + n
Batya's age in n years = 7 + n
Noam's age = 4 x Batya's age
43 + n = 4(7 + n)
n = 5
So in 5 years Noam will be 48 and Batya will 12
2(4x + 3) = 5(x + 3)
x = 3
(x + a)/ b = c
x = cb - a
5(2x + 3) - 4x = 3(2x + 5)
6x + 15 = 6x + 15
0 = 0
There are infinite solutions!
-2x + 5 < 15 and x <= 7
Plot in a number line
Write as a singular inequality
Interval Notation
x > -5 and x < 7
Singular Inequality: -5 < x < 7
Interval notation (-5, 7]
We will draw the number line on the board.
Write as an inequality and solve
When three times a number n is increased by 12, the result is at least 32.
3n + 12 > 32
3n > 20
n > 20/ 3
1/2(2x - 6) = 2x - 15
x = 12
(x +a)/b - c = d
x = b(d + c) - a
1/2(2x - 6) = x - 3
x - 3 = x -3
0 = 0
Infinite solutions!
-2(5x + 5) >= 40 and x > -10
Plot on a number line
Write as a single inequality
Interval Notation
x <= -5 and x > -10
Single Inequality : -10< x <=-5
Interval Notation: (-10, -5]
We will draw the number line on the board.
A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel?
1.75 + 0.65x < 10
At least 12 more sessions