SOLUTION: Help!!!!!!!! (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).

Algebra.Com
Question 974807: Help!!!!!!!!
(4 - x ≤ -1) ∩ (2 + 3x ≥ 17).
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
(4 - x ≤ -1) ∩ (2 + 3x ≥ 17).

(-x ≤ -5) ∩ (3x ≥ 15).

The inequality reverses in the left part since we are dividing 
through by a negative number -1.

(x ≥ 5) ∩ (x ≥ 5).

Draw each part on a number line

-------------------------------@===========>  That's x ≥ 5
-5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9


-------------------------------@===========>  That's x ≥ 5 
-5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

Intersection ∩ means to use ONLY the part where the two
graphs overlap, that is, the part of the number line where
BOTH are true and darkened or shaded ===.  @ means a darkened circle.

But they (overlap) intersect EVERYWHERE!!!

-------------------------------@===========>
-5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

So that is x ≥ 5, which in scientific notation is [5,oo)
where oo indicates "infinity".

Edwin
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
(4 - x ≤ -1) ∩ (2 + 3x ≥ 17).

(-x ≤ -5) ∩ (3x ≥ 15).

The inequality reverses in the left part since we are dividing 
through by a negative number -1.

(x ≥ 5) ∩ (x ≥ 5).

Draw each part on a number line

-------------------------------@===========>  That's x ≥ 5
-5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9


-------------------------------@===========>  That's x ≥ 5 
-5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

Intersection ∩ means to use ONLY the part where the two
graphs overlap, that is, the part of the number line where
BOTH are true and darkened or shaded ===.  @ means a darkened circle.

But they (overlap) intersect EVERYWHERE!!!

-------------------------------@===========>
-5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

So that is x ≥ 5, which in scientific notation is [5,oo)
where oo indicates "infinity".

Edwin
RELATED QUESTIONS

Solve 3x - 4 ≤ 2 or 2x + 11 ≥ -1. a. {x | x ≤ 2} b. {all reals}... (answered by tommyt3rd)
Solve 3x - 4 ≤ 2 or 2x + 11 ≥... (answered by tommyt3rd)
Solve the following system of inequalities by graphing. draw a graph 5x - 4y ≥ -20 (answered by MathLover1)
Sketch a graph of the inequality. 1.) 0 ≤ x + 9 < 17 2.) x - 4 < -12 or 2x... (answered by lwsshak3)
determine the point of intersection of: a) 1/2(x-2)-1/4(3-y) ≥ 2 (answered by MathLover1)
1) x ≤ 3y, x≥y. (2) y ≥ 2x, −2x+3y ≤6. (3) 3x +5y ≥... (answered by Shin123,ikleyn)
I need help solving these problems, could you help?? 1. Solve: |3x+2|>4 A. x < -2 (answered by Alan3354)
I don't understand these types of problems? Please help! Graph each system of... (answered by Alan3354)
Help Needed; Graph the feasible region for the system of inequalities. 2y + x... (answered by jim_thompson5910)