Final Review Math 125
Combine and simplify
Solve
3
2
(x  1)
Simplify
1
3
(x  1)
2x  1 x  1

x 3 x2
3
3
= 2
x2
x
A group of x people rent a bus that cost $36 and share the cost. If three more people join the group,
then each person would pay $1 less. Set up an equation and solve for x.
Solve for x:
x+5 = 2  x
If the solutions are real numbers, give the simplified exact solution and the numerical approximation. If
the solutions are complex, just simplify the solutions.
2x (x + 1) = 3 + x
2x2 + 2x + 3 = 0
2x (x – 1) = 2x + 1
2x2 + 4(x – 3) = 4x
Rationalize the denominator
3 2
23 2
Solve the following inequalities. Draw the solution on a line. Indicate clearly if the end points are included.
x2 – 5x ≥ –6
𝑥(𝑥–3)
𝑥+2
≤0
Graph the quadratic equations y = –x2 + 6x – 8. Draw the line of symmetry.
Find and label the vertex. Label the x and y intercepts, if any.
Circles and completing the square method
(No calculator)
Solve 92x – 2 3x = 271 – x
Solve log3 (2x + 7) + log3 (x + 2) = 3
Give the exact and approximate answers (to 3 significant digits) with a calculator.
6. 7 – 3 *e2x = 4
7. 15 = 25 – 6 log(3x + 1)
8. 3(9 2x +1 ) = 20
Let f(x) = –x2 + x, g(x) = –2x + 4 and h(x) = 5 – 3x, find the following.
5. h(–2) + 2g(0)
6. g(a + 3) + h(a – 3)
7. f(a – b) – f(a)