equations & inequalities (one variable, linear)
3(q − 7) = 27
q = 16
−9x − 6y = 15
9x − 10y = 145
x = 5
y = -10
Is (-4 , -4) a solution to the inequality y > −6x − 1
No
y = 2x + 1
(x + 1)^2 + y^2 = 1
Find both solutions
(-1 , -1)
(-0.2 , -0.6)
4x − 32
x^2 − 64
Reduce the Rational expression to lowest terms
4 / x + 8
16 − 2t = t + 9 + 4t
t = 1
6x − 2y = 8
4x − 3y = 2
x = 2 , y = 2
Is (1 , -2) a solution to the system of inequalities
9x + 4y < 8
−3x − 7y ≥ 5
Yes
x − y = −4
y = 5(x + 1)^2 − 3
(-2 , 2)
(0.2 , 4.2)
2x^2 + 4x
x^2 + 5x + 6
2x / x + 3
−67b + 6 ≤ 9b + 43
b ≥ −37/76
4x + 3y = 19
−x + 4y = 0
x = 4 , y = 1
Is (-4 , 2) a solution to the inequality
4x + 5y ≤ −7
No
2x + y = −4
y = (x + 1)^2 − 2
(-3 , 2)
(-1 , -2)
x − 3 / x + 1 = 4x − 6 / (x + 1)(x + 2)
Solve the Rational equation
x = 0 , 5
11q + 5 ≤ 49
q ≤ 4
6x + y = 15
−7x − 2y = −10
x = 4 , y = −9
Horace is a professional hair stylist. Let C represent the number of child haircuts and A represent the number of adult haircuts that Horace can give within 7 hours. 0.75C + 1.25A ≤ 7
Horace gave 5 child haircuts. How many adult haircuts at most can he give with the remaining time?
At most 2 adult haircuts
x^2 + y^2 = 1
y = 2x + 2
(-1 , 0)
(-0.6 , 0.8)
x + 1 / x − 3 = −x^2 − 6x + 1 / (x − 3)(x − 1)
x = 0
−9x + 5 < 17 AND 13x + 25 < −1
No Solutions
x + 2y + 5z = -17
2x − 3y + 2z = -16
3x + y − z = 3
x = -1
y = 2
z = -4
An electric filter purifies air at the rate of 35 liters per minute and uses energy at the rate of 0.8, point, 8 Joules per minute. It also purifies water at the rate of 25 liters per minute and uses energy at the rate of 1.3 Joules per minute. The filter is expected to purify more than 1000 liters of air and water while using less than 170 Joules of energy. Let A denote the number of minutes it spends purifying air and W the number of minutes it spends purifying water. Write a System of inequalities to represent this .
35A + 25W > 1000
0.8A + 1.3W < 170
(x − 1)^2 + (y − 1)^2 = 1
y = 2x + 1
(0 , 1)
(0.4 , 1.8)
f(x) = 6x^3 − x^2 + 7 / 2x + 5
f(x) = ∞ ,x = -∞
f(x) = ∞ ,x = ∞