Answer:
Part 41) The solution of the compound inequality is equal to the interval [-1.5,-0.5)
Part 45) The solution of the compound inequality is equal to the interval
(-∞, -0.5] ∪ [1,∞)
Step-by-step explanation:
Part 41) we have
[tex]-4\leq 2+4x < 0[/tex]
Divide the compound inequality into two inequalities
[tex]-4\leq 2+4x [/tex] -----> inequality A
Solve for x
Subtract 2 both sides
[tex]-4-2\leq 4x [/tex]
[tex]-6\leq 4x [/tex]
Divide by 4 both sides
[tex]-1.5\leq x [/tex]
Rewrite
[tex]x\geq -1.5[/tex]
The solution of the inequality A is the interval -----> [-1.5,∞)
[tex] 2+4x < 0[/tex] -----> inequality B
Solve for x
Subtract 2 both sides
[tex]4x < -2[/tex]
Divide by 4 both sides
[tex]x < -0.5[/tex]
The solution of the inequality B is the interval ------> (-∞, -0.5)
The solution of the inequality A and the Inequality B is equal to
[-1.5,∞)∩ (-∞, -0.5)------> [-1.5,-0.5)
see the attached figure N 1
Part 45) we have
[tex]2x-3\leq -4[/tex] or [tex]3x+1\geq 4[/tex]
Solve the inequality A
[tex]2x-3\leq -4[/tex]
Adds 3 both sides
[tex]2x\leq -4+3[/tex]
[tex]2x\leq -1[/tex]
Divide by 2 both sides
[tex]x\leq -0.5[/tex]
The solution of the inequality A is the interval ------> (-∞, -0.5]
Solve the inequality B
[tex]3x+1\geq 4[/tex]
Subtract 1 both sides
[tex]3x\geq 4-1[/tex]
[tex]3x\geq 3[/tex]
Divide by 3 both sides
[tex]x\geq 1[/tex]
The solution of the inequality B is the interval -----> [1,∞)
The solution of the compound inequality is equal to
(-∞, -0.5] ∪ [1,∞)
see the attached figure N 2
