SECTION 3.4 Linear Inequalities in Two Variables 179
For Discussion or Writing
Solve the equation in part (a) and the associated inequalities in parts (b) and (c), by
graphing the left side as yin the standard viewing window of a graphing calculator.
Explain your answers using the graph.
1. (a) (b) (c)
2. (a) (b) (c)
3. (a) (b)
(c)
4. (a) (b)
(c) - 4 x- 12 x+ 182 ... 0
- 4 x- 12 x+ 182 = 0 - 4 x- 12 x+ 182 Ú 0
- 8 x- 12 x+ 122 ... 0
- 8 x- 12 x+ 122 = 0 - 8 x- 12 x+ 122 Ú 0
6 x+ 3 = 0 6 x+ 37 0 6 x+ 360
5 x+ 3 = 0 5 x+ 37 0 5 x+ 360
Complete solution available
on the Video Resources on DVD
3.4 EXERCISES
Concept Check In Exercises 1– 4, fill in the first blank with either solidordashed. Fill in
the second blank with eitheraboveorbelow.
1.The boundary of the graph of will be a line, and the shading will be
the line.
2.The boundary of the graph of will be a line, and the shading will be
the line.
3.The boundary of the graph of will be a line, and the shading will be
the line.
4.The boundary of the graph of will be a line, and the shading will be
the line.
5.How is the boundary line used in graphing either or
?
6.Describe the two methods discussed in the text for deciding which region is the solution
set of a linear inequality in two variables.Graph each linear inequality in two variables. See Examples 1 and 2.Graph each compound inequality. See Example 3.- and 24. and
- and 26. and
27.x+y7- 5 and y6- 2 28. 6 x- 4 y 610 and y 72
2 x-yÚ 2 y 64 3 x-yÚ 3 y 63x+y... 1 xÚ 1 x-yÚ 2 xÚ 3x- 3 y... 0 x- 5 y... 0 y 6 x y... 4 x4 x- 5 y 720 x+y 70 x+ 2 y 702 x+ 3 yÚ 6 3 x+ 4 yÚ 12 5 x- 3 y 7153 x-y 63 x+ 3 yÚ- 2 x+ 4 yÚ- 3x+y... 2 x+y...- 3 4 x-y 64Ax+By 7 CAx+By=C Ax+By 6 CyÚ-x+ 2y7-x+ 2y6-x+ 2y...-x+ 2