Find all values that satisfy the inequality  2x+5 =< 4(x-1)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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).

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