I 2x+3 I + 5 ≥ 9 solve the inequality?

Question

francisco

Answer 1

| 2x + 3 | + 5 ≥ 9
| 2x + 3 | ≥ 4
±(2x + 3) ≥ 4
+(2x + 3) ≥ 4 or -(2x + 3) ≥ 4 [Remember that with absolute value inequalities, > or ≥ makes an "OR" statement, while < or ≤ makes an "AND" statement for your compound inequality. Think "GreatOR" or "LessthAND."]
2x + 3 ≥ 4 or -2x - 3 ≥ 4
2x ≥ 1 or -2x ≥ 7
x ≥ 0.5 or x ≤ -3.5 [Remember that when multiplying both sides of an inequality by a negative number, the inequality changes.]

When graphing your solution set for x on a number line, there is a "hole" between -3.5 and 0.5... all numbers to the left and including -3.5 should work, as well as 0.5 and all numbers to its right. In interval notation, x can be
(-∞, -3.5] or [0.5, ∞).

As a quick check to your answer, any number between -3.5 and 0.5 chosen for x must make the original absolute value inequality a FALSE statement. Choosing 0 for x, for example, means
| 2(0) + 3 | + 5 = | 0 + 3 | + 5 = | 3 | + 5 = 3 + 5 = 8. 8 is not ≥ 9, so the statement is indeed false for a number between -3.5 and 0.5.

Answer 2

I 2x+3 I + 5 ≥ 9
I 2x+3 I ≥ 4

2x+3 ≥ 4 or 2x+3 ≥ -4
2x ≥ 1 or 2x ≥ -7
x ≥ 1/2 or x ≥ -7/2

Answer 3

The key to solving any inequality with absolute values is to isolate the absolute value on one side, and then make two separate equations for the two "values" (positive and negative) of the inequality. Let me give a simple example:

|x-2| < 10

To solve, you solve these two inequalities:

(x-2) < 10

and

-(x-2) < 10

The answer will be the two inequalities combined together. Just don't forget when solving the two sides that when you multiply or divide both sides of an inequality by a negative number, you have to switch the direction of the inequality.

Answer 4

x ≥ -2 1/4

Answer 5

x<1/2 or X>-7/2

Answer 6

take care of the inequality signal as if it were an equivalent signal. 13.) 5x>2x+9 combine like words -2x -2x 3x>9 divide by 14.) -3x+3>9 combine like words -3x>6 divide by x>-2 with a unfavorable answer, swap the inequality signal round. 15.) 4x-5>2x+3 combine like words 2x>8 divide by

Answer 7

x> 1/2, don't know how to type the inequality sign on my computer, but it's less than equal to 1/2, no that's not right, sorry i suck at math, 2/3 +5 (inequality sign) 9 and do the addition.???????

Answer 8

x≥1/2 I thought I'd come back and show my work


I 2x+3 I + 5 ≥ 9
-5 -5 subtract 5 from both sides
______________
2x +3 ≥ 4 remove absolute value signs
-3 -3 subtract 3 from both sides
2x ≥ 1 then divide by 2
x ≥ 1/2

Answer 9

|2x + 3| + 5 >= 9
|2x + 3| >= 4
2x + 3 >= 4 or 2x + 3 <= -4
2x >= 1 or 2x <= -7
x >= (1/2) or x <= (-7/2)

Answer 10

|2x+3| ≥ 9-5
so square both sides (2x+3)^2 ≥ 4^2
4x^2 + 12x + 9 ≥ 16
4x^2 + 12x - 7 ≥ 0
(2x + 7)(2x - 1) ≥ 0
:. x <= -7/2 or x ≥ 1/2