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-5x + 8 ? 3x + 8 (please explain solving this)

-5x + 8 ? 3x + 8 (please explain solving this)
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That helps.
 
So first you want to get EVERYTHING with an x on one side. So let's subtract 3x from BOTH sides
5x-3x+8≥3x-3x+8
 
So now combine the like terms-> 5x-3x=2x  AND 3x-3x=0
 
2x+8≥8  Now we need to get x by itself. This is solved EXACTLY like and equation.
 
Subtract 8 from BOTH sides
 
2x+8-8≥8-8
2x+0≥0
2x≥0  STILL NOT by itself.  Divide BOTH sides by 2.
 
(2x)/2≥0/2
(2/2)x≥0/2    2/2=1   0/2=0
x≥0
 
This is saying that to make the ORIGINAL STATEMENT true, you can use ANY number BIGGER than OR EQUAL to 0. examples-> 0, 1, 2, .5, .25, 500, etc
 
 
 
 

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1 Answer


Solving inequality is very like solving equation. The only difference: if divide or multiply both sides of inequality by negative number, we have to change sign of inequality to opposite.
~~~~~~~~~~

-5x + 8  ≥  3x + 8
       - 8           - 8

- 5x   ≥   3x
- 3x      - 3x

   - 8x   ≥    0
÷(- 8)    ÷(- 8)

    x ≤ 0  ,  or all real numbers out of interval (- ∞, 0]

 <====|=====———|————>

- ∞    - 10         0       10       + ∞


Let's verify the answer:

for x = -10,

-5 × (-10) + 8 ≥ 3 × (- 10) + 8
           50 + 8 ≥ -30 + 8
                 42 ≥ - 22    (True)

for x = 10,

- 5 × 10 + 8 ≥ 3 × 10 + 8
      - 50 + 8 ≥ 30 + 8
            - 42 ≥ 38     (False)