Solve the following polynomial inequality: 4x - 5 <= 2(x-7)Show all your work

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jeew-m's profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

4x-5 <=2(x-7)

 

First lets expand the brackets

4x-5 <= 2x-2*7

 

Now lets subtract 2x from both sides.Then the right side x terms will be vanished

4x-5-2x <= 2x-14-2x

    2x -5 <= -14

 

Now lets add 5 to both sides which will isolate the x terms in left side

2x-5+5 <= -14+5

        2x <= -9

 

Not both sides will be divided by 2 to have x only in left side.

 2x/2 <= -9/2

      x <= -9/2

 

4x-5 <=2(x-7) inequality will be satisfied when x is lesser or equal to -9/2. So x can have values -9/2 to - `oo` .

We can write it as follows.

 `x in (-oo,-9/2]`

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odette95 | Student, Undergraduate | (Level 1) eNoter

Posted on

4x - 5 <= 2(x-7)

 

Solve this by changing the inequality sign to an equal sign, so we have:

4x-5=2(x-7)

Distribute 2 to the parenthesis:

4x-5=2x-14

Combine like terms, that is; those which contains variables should be on the LEFT SIDE of the equation and constants should be on the RIGHT SIDE:

4x-2x=-14+5

2x=-9

Divide both sides by 2:

x= -4.5

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