We have to find all values of x that satisfy 2x+5 =< 4(x-1)
2x+5 =< 4(x-1)
open the brackets
=> 2x + 5 =< 4x - 4
move the terms with x to one side and the numeric numeric terms to the other
=> 2x - 4x =< -4 - 5
=> -2x =< -9
=> 9 =< 2x
=> 9/2 =< x
Therefore x >= 9/2
2x + 5 =< 4(x-1)
We need to find x values.
We will solve the same way we solve the equation.
The goal is to isolate x on one side.
First we will open the brackets on the right side.
==> 2x + 5 =< 4x -4
Now we will subtract 4x from both sides.
==> -2x + 5 =< -4
Now we will subtract 5 from both sides.
==> -2x =< -4 -5
==> -2x =< -9
Now we will divide by -2 and reverse the inequality.
==> x >= 9/2
Then the values of x that satisfies the inequality should be equal or greater that 9/2.
==> x belongs to the interval [ 9/2, inf).