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Tema [17]
3 years ago
10

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

Mathematics
1 answer:
Oksanka [162]3 years ago
4 0

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

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