Linear & Structure
3(2x - 1) - 4x = 5
6x − 3 − 4x = 5
2x − 3 = 5
2x = 8
x = 4
x^2 − 9
(x − 3)(x + 3)
(x^3y^2)(x^2y^4)
x^5y^6
If f(x) = 2x² − 3x + 1, find f(2).
8 − 6 + 1 = 3
If 4x − 7 = 3x + 5, what is x?
x − 7 = 5
x = 12
x^2 − 5x + 6 = 0
x = 2, 3
6sqrt2
If f(x) = 3x + 4 and f(a) = 19, find a.
a = 5
(4x + 6)/2 = x + 5
Multiply both sides by 2:
4x + 6 = 2x + 10
Subtract 2x:
2x + 6 = 10
Subtract 6:
2x = 4
x = 2
2x^2 − 8 = 0
2x^2 = 8
x^2 = 4
x = ±2
√(x + 5) = 4
x + 5 = 16
x = 11
If: 3x + 4 = kx − 8 has no solution, what is k?
For no solution:
The coefficients of x must be equal,
but constants must be different.
So:
3 = k
Since 4 ≠ −8, the equation has no solution.
x^2 + kx + 4 = (x + 2)^2
Expand the right side & match.
k = 4
(3x²y⁻¹)/(6xy²)
x/(2y³)
If f(x) = 1/x, what is f(2x)?
1/(2x)
Solve for x:
x/(x − 3) = 2
x = 2(x − 3)
x = 2x − 6
x = 6
If one solution to x^2 − 7x + c = 0 is 3, find c.
Plug in 3:
9 − 21 + c = 0
c = 12
If 2^(x+1) = 16, find x.
16 = 2⁴
x + 1 = 4
x = 3
If f(x) = ax² and f(3) = 27, find a.
a=3