Factoring: 1. find the two numbers that multiply to equal ac (2 • 2) and add to equal b (-5) The numbers = -4, -1
2. Extend the b term into these two numbers. 2x^2 -4x - x + 2
3. Group the first two terms and the last two terms to each other. (2x^2 - 4x)(-x + 2)
4. Take out the GCF's in the parentheses sections. Note: the terms inside both of the parentheses should be equal, or you have done something wrong. 2x(x - 2) - 1(x - 2)
5. Group the GCF's together alongside the equivalent parentheses sections. (2x - 1)(x - 2)
You're done here, but IF you want to find the solutions, you have to set each of the new parentheses sections to zero and solve for x. 2x - 1 = 0 >> 2x = 1 >> x = 1/2 x - 2= 0 >> x = 2
In conclusion, your solutions are x = 1/2 and x = 2, and your factored equation is (2x - 1)(x - 2)
2(4+2x)≥5x+5 4+2x≥5/2x+5/2 (divide both sides by 2) 3/2+2x≥5/2x (subtract 5/2 from both sides) 3/2≥1/2x (subtract 2x from both sides) 3≥x (multiply both sides by 2) or x≤3
