Linear Equations and Inequalities
Solve for x:
2x + 5 = 15
x=5
What's the vertex form of a quadratic function?
y=a(x-h)2+k
What's the common base for natural logarithms?
Solve the system:
2x + y = 7
x - y = 1
(2,1)
x=2
y=1
What's the degree of a polynomial?
The Highest Exponent
Solve the inequality:
3x - 7 > 2x + 4.
x>11
Factor the quadratic expression:
x2 + 5x + 6.
(x+3)(x+2)
Solve for x:
32x= 27.
x=3/2
x=1.5
Solve the system:
2x - y = 8
x + 2y =4
(4,0) or
x=4
y=0
Perform the operation:
(3x² - 2x + 5) + (x² + 3x - 1).
4x2 + x + 4
Write the equation of a line in slope-intercept form that passes through (3, -2) and with a slope of 2
y=2x-4
Solve for x:
x2 - 9 = 0
x=3
x=-3
Simplify the logarithmic expression:
log₂(4) + log₂(8)
log2(32)
Classify the system as consistent independent, consistent dependent, or inconsistent:
3x - 2y = 5
6x - 4y = 10
Consistent Dependent
Factor the polynomial:
x3 - 8
(x - 2)(x2 + 2x + 4)
Solve the equation:
4(2x - 1) = 2(3x + 2)
x=4
Find the axis of symmetry of the parabola:
y = -2x2 + 8x - 5
Axis of Symmetry is
x=2
Solve the equation:
e2x = 25
x=ln(25)/2
Solve the system using the substitution method:
4x - y = 7
x + 2y = 5
(3,5) or
x=3
y=5
Divide the polynomials:
(3x3 - 9x2 + 6x) / (x - 2)
3x2 - 3x
Solve the system of equations:
3x - y =9
2x + y = 6
(0,3) or
x=0
y=3
Complete the square to find the solutions of:
x2 - 6x + 9 = 0
x=-3
Express the logarithmic equation log₅(25) = x in exponential form.
5x=25
Solve the system using the elimination method
2x - 3y = 10
4x - 6y = 20
Consistent Dependent
Find all the roots (real or complex) of the polynomial equation:
x4 - 10x² + 9 = 0
x = -3, -1, 1 , 3