Solve each inequality, graph each solution, and give interval notation.

Question

5m+4 ≤ -11

 

Graph inequalities using this notation: < ----------(========= >

                                                                        3

 

 

 

Answer 1

Treat the inequality like a regular equation until you have to divide or multiply by a negative number, then the sign would flip. Begin by subtracting 4 from both sides. Next step is to divide both sides by 5. Since you're dividing by a positive number, the arrow does NOT flip. Keep in mind that the variable is the shaded part on the graph. Since m is less than OR EQUAL TO -3, the shading would start on -3 on the number line, and go left. 

Remember that in interval notation, parentheses are used next to infinities and numbers that ARE NOT included or equal to the solution. We will use a bracket in our final answer. (-∞,-3] would be the answer in the form of interval notation.

Answer 2

To add to Steve's answer:

 

In interval notation,

 

(-∞, 3]

 

 

The bracket indicates that 3 is included in the solution set.

 

Answer 3

5m+4 ≤ -11  -->  5m ≤ -15  -->  m ≤ -3

 

Graphed as :                      <=================]---------------------->

                                                                                  -3