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Final Review Math 125 Combine and simplify Solve 3 2 (x 1) Simplify 1 3 (x 1) 2x 1 x 1 x 3 x2 3 3 = 2 x2 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 23 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)