Question

Can someone please do 41 and 45???? Thanks!!!

Answer 1

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

$-4\leq 2+4x < 0$

Divide the compound inequality into two inequalities

$-4\leq 2+4x$ -----> inequality A

Solve for x

Subtract 2 both sides

$-4-2\leq 4x$

$-6\leq 4x$

Divide by 4 both sides

$-1.5\leq x$

Rewrite

$x\geq -1.5$

The solution of the inequality A is the interval -----> [-1.5,∞)

$2+4x < 0$ -----> inequality B

Solve for x

Subtract 2 both sides

$4x < -2$

Divide by 4 both sides

$x < -0.5$

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

$2x-3\leq -4$  or $3x+1\geq 4$

Solve the inequality A

$2x-3\leq -4$

Adds 3 both sides

$2x\leq -4+3$

$2x\leq -1$

Divide by 2 both sides

$x\leq -0.5$

The solution of the inequality A is the interval ------> (-∞, -0.5]

Solve the inequality B

$3x+1\geq 4$

Subtract 1 both sides

$3x\geq 4-1$

$3x\geq 3$

Divide by 3 both sides

$x\geq 1$

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