1.Algebra Booster

Quadratic Equations and Expressions 2.13
166.
2013 2014
( x -1) ( x -2)
( x -3) ( x -5)
2016 2010
> 0
167. x 2 (x – 1) > 0
168. x 2 (x – 1) 10 (x + 2) 11 > 0
4 12
( x -1) ( x -2)
169.
> 0
17 2012
( x -3) ( x -5)
201 2012
( x+ 1) ( x -4)
170.
> 0
2012 2013
( x+ 3) ( x -2)
1
171. 1 0
2
x - ≥
172. x 3 – 3x + 2 ≥ 0
173. x 3 + 7x 2 – 36 ≥ 0
Type V: If f(x) = ax 2 + bx + c, where a > 0 and D < 0, then
we discard it
Solve for x:
174. x 2 + x + 2 > 0
175. x 2 – x + 3 < 0
176. (x + 2_(x 4 + x 2 + 1) > 0
177. x 4 – 4 £ 0
178. (x 2 + 4x + 1)(x 2 + 1) ≥ 0
179. (x – 2)(x 2 + x + 2) > 0
180. (x – 3)(–x 2 + x + 1) > 0
181. x 3 + 4x ≥ 0
182. x 4 – 9 ≥ 0
183. x 3 – 5x + 4 ≥ 0
184. x 3 – 3x 2 + 3x – 9 ≥ 0
185. x 3 – 6x 2 + 12x – 9 ≥ 0
186. 2x 2 + 5x > 12
187. 4x 2 + 4x + 1 £ 0
Type VI: Common values of x in
f(x) ≥ 0 and g(x) ≥ 0
or
f(x) ≥ 0 and g(x) £ 0
Q. Solve for x:
188. x 2 – 3x + 2 > 0, x 2 + 2x – 8 < 0
2 2
189. x - 9£ 0, x -1≥0
190.
191.
192.
193.
194.
195.
196.
197.
3 3
x -9x≥ 0and x + 4x£
0
2 2
x - 4x+ 3≥0and x - 4£
0
2 2
x -9≥0and x - 4£
0
2 2
x - 6x+ 8 ≥0 and x - 3x+ 2 ≥0
2 2
x - 5x+ 6 ≥0 and x - 10x+ 24 £ 0
2 2
x - x≥0 and x - 12x+ 27 £ 0
3 2
x + x≥0andx
- 9£
0
3 3
x -9x≥ 0and x + 4x£
0
EQUATION CONTAINING ABSOLUTE VALUES
198. Solve for x: |x| 2 – 3|x| + 2 = 0
199. Find the sum of the roots of x 2 – 4|x| + 3 = 0
Solve for x:
200. |3x – 1| = |x + 5|
201. |2x – 5| = x – 3
202. |x 2 – x – 6| = x + 2
203. 2|x – 2| + 3|x – 4| = 3
204. |x| + |x – 2| = 4
205. |x – 1| + |x – 3| = 2
206. |x 2 – 1| + |x 2 – 4| = 3
207. x+ 2 x - 1 + x -2 x - 1 = 2
208.
x x
+ | x|
=
x -1 | x-1|
| x 1| x
209. 2 + x
- 2 = |2 - 1| + 1
210. |x 2 + x – 20| = –(x 2 + x – 20)
Ê
2 2
x - 6x+ 8ˆ Ê x - 6x+
8ˆ
211. Á 2 ˜ =-Á 2 ˜
Ë x - 4x+ 3¯ Ë x - 4x+
3¯
INEQUALITIES WITH THE ABSOLUTE VALUE
Solve for x:
212. |x – 1| < 3
213. |x – 4| £ 3
214. |x + 2| > 5
215. |x – 2| ≥ 3
4x - 2
216. £ 2
3
217. x 2 – |3x – 2| > 0
218. |x| + |x – 2| > 3
219. |x + 2| + |x| + |x – 2| > 6.
2
220. £ 1
x + 3
221. |3x + 2| > |2x – 1|
IRRATIONAL EQUATIONS
Solve for x:
222. (2x+ 7) + ( x+ 4) = 0
223. ( x - 4) = -5
224. ( x -6) - (8- x) = 2
225. (-2- x) = 5 (x -7)
226. x + ( x+ 16) = 3
15
227. 7 x + 8 - x + = 98.
3
x
228. x - 2 + 4- x = 6-
x
229. 2 x – 4 - x+ 5 = 1
230. 3x+ 4 + x - 4 = 2 x
231. x - 1+ 2x+ 6 = 6
2