-16/3 < x < 8/3
-9/4 < x < 15/4
-15/4 < x < 9/4
-8/3 < x < 16/3
or is it none of these
2007-01-27 02:39:29 · 7 answers · asked by Olivia 4 in Science & Mathematics ➔ Mathematics
|4x + 3| < 12
We can write as below
4x + 3 < 12 or -(4x+3) < 12
4x + 3 < 12
4x < 9
x < 9/4
-(4x+3) < 12
4x > -15
x > -15/4
So, -15/4 < x < 9/4
2007-01-27 02:48:00 · answer #1 · answered by seah 7 · 1⤊ 0⤋
Absolute value is a distance from a point on the number line. Suppose, for example, you were standing on point 0 on the number line. This equation means that I can be standing anywhere within 12 steps of you to the right of the number line (less than +12): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11; or anywhere within 12 steps of you to the left of the number line (greater than -12): -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0.
Writing these words as a mathematical expression, we get:
|4x + 3| < 12
-12 < 4x + 3 < 12
-15 < 4x < 9
-15/4 < x < 9/4
2007-01-27 02:50:11 · answer #2 · answered by ybdogsct 2 · 1⤊ 0⤋
-15/4
2007-01-27 02:47:58
·
answer #3
·
answered by dave l 1
·
0⤊
0⤋
4x+3<12 4x+3>-12
9/4 , -15/4
-15/4 < x < 9/4
2007-01-27 02:44:38 · answer #4 · answered by airhead15274 1 · 1⤊ 0⤋
-15/4 < x < 9/4 is the range of real solutions for x when
|4x + 3| < 12 is true
2007-01-27 02:56:18 · answer #5 · answered by michaell 6 · 0⤊ 0⤋
|4x + 3| < 12
By definition of the absolute value, this means
-12 < 4x + 3 < 12
Our goal is to isolate the x term in the inequality. To do so, we must first subtract 3 from the inequality.
-12 - 3 < 4x < 12 - 3
Solving, we get
-15 < 4x < 9
Now, we divide by 4 to the inequality.
-15/4 < x < 9/4
2007-01-27 02:46:48 · answer #6 · answered by Puggy 7 · 1⤊ 0⤋
none.
2007-01-27 02:47:32 · answer #7 · answered by RiRi 3 · 0⤊ 1⤋