Solve the following polynomial inequality: 4x - 5 <= 2(x-7)Show all your work
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]`
4x - 5 <= 2(x-7)
Solve this by changing the inequality sign to an equal sign, so we have:
Distribute 2 to the parenthesis:
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:
Divide both sides by 2: