Linear Equations
Solve:
3x - 7 = 12x + 3
-10 = 9x
x = -10/9
Solve:
x² - 529 = 0
x = ±23
Write an equation to find the terms for the following sequence.
8, 3, -2, -7, ...
A(n) = 8 + (-5)(n-1)
Solve:
5(2x - 3) > 4x + 6
x > 7/2
Is the relation a function?
{(2,3), (8,5), (4, 8), (3, 2), (5, 4), (2, 5)}
No!
Solve:
2(3x + 5) = -4(x - 4)
10x = 6
x = 3/5
y = 12x - 3x²
x = -b/(2a) = -12/(2*-3) = -12/(-6) = 2
y = 12(2) - 3(2)² = 12
Vertex: (2, 12)
Solve:
(x - 3)/x = 9/10
10(x - 3) = 9x
10x - 30 = 9x
x = 30
Solve:
6x - 2 ≤ -5 OR 3x + 4 > 9
x ≤ -1/2 or x > 5/3
149.5 is what percent of 130?
115%
Write the equation of a line with slope -1/2 passing through the point (2,3).
Point-slope form: y - 3 = -1/2(x - 2)
Slope - intercept form: y = -1/2x + 4
How many solutions does the equation have?
10x² = 22x - 4
10x² - 22x + 4 = 0
b² - 4ac = (-22)² -4(10)(4) = 324
Two real solutions!
Solve the system:
4x - 8y = 5
6x - 12y = 10
No solution!
Solve:
120 < 20x - 40 ≤ 160
8 < x ≤ 10
Solve the system:
4x - 3y = -13
5x + 6y = 13
(-1, 3)
Write the equation of the line passing through (9, 2) and (9, 5).
It’s a vertical line (slope is undefined)!
x = 9
Solve:
4x² - 9 = 0
We could solve using square root, factoring, or quadratic formula!
x = ±3/2
Solve:
8x³ + 12x² - 2x - 3 = 0
Factor to (4x² - 1)(2x + 3) = 0
x = ±1/2, -3/2
Solve:
|2x - 1| < 9
2x - 1 < 9 OR 2x - 1 > -9
-4 < x < 5
Evaluate f(-1)
f(x) =
2x³ if x < -3
3x - 1 if -3 ≤ x ≤ 3
-2x² + 4 if x > 3
f(-1) = 3(-1) - 1 = -4
Write the equation of the line passing through (-4, 5) and perpendicular to 3x + 2y = -8.
Point-slope form: y - 5 = 2/3(x + 4)
Slope-intercept form: y = 2/3x + 23/3
Solve:
3x² - 6x = 12
3x² - 6x - 12 = 0
x = 1 ± √5
Solve the equation:
√(3 - 11x) = 2x
3 - 11x = 4x²
0 = 4x² + 11x - 3
x = -3, 1/4 —> -3 doesn’t work!
Solution: x = 1/4
Solve:
|3x + 4| - 5 > 0
|3x + 4| > 5
3x + 4 > 5 OR 3x + 4 < -5
x > 1/3 OR x < -3
What are the horizontal AND vertical asymptotes for
y = (3x² - 3x + 4)/(x² - 1)
Vertical: x = ±1
Horizontal: y = 3