Solve the inequality : 2x+3 =< 13

### 4 Answers | Add Yours

Given the inequality: 2x+3 =< 13

We need to find all possible x values that satisfies the inequality.

First we will need to isolate x on the left side.

==> 2x+3 =< 13

Subtract 3 from both sides.

==> 2x =< 10

Now we will divide by 2.

==> x =< 5

Then, the equality holds for all x values equal or less than 5.

**==> x = ( -inf, 5] **

We have to solve 2x + 3 <= 13

2x + 3 <= 13

=> 2x =< 13 - 3

=> 2x =< 10

=> x =< 5

**The value of x lies in (-inf. , 5]**

All we need to know is to determine the segment of the line that is below x axis. For this reason, we'll find out x values that makes the expression of the linear function to be negative:

2x + 3 - 13 =< 0

2x - 10 =< 0

2x =< 10

x =< 5

**The values of x, for the segment of linear function is found below x axis, are located in the semi-closed interval (-infinite , 5].**

The inequality 2x+3 =< 13 has to be solved.

If an equal term is added or subtracted from both the sides of an inequality, it is not altered.

2x+3 =< 13

Add -3 to both the sides.

2x+3-3 =< 13-3

2x <= 10

If the sides of an inequality are divided by a positive term it is not altered.

Divide the two sides of the inequality by 2

x <= 10/2

x <= 5

The solution of the inequality is all values of x less than or equal to 5.

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes