Question

Solve the inequality. 4x + 1 < 8x - 3 < 4x + 5

Answer 1

Answer:

1 <x <2

Step-by-step explanation:

4x + 1 < 8x - 3 < 4x + 5

Split into two inequalities

4x + 1 < 8x - 3           and        8x - 3 < 4x + 5

Do the first one first

4x + 1 < 8x - 3

Subtract 4x from each side

4x -4x + 1 < 8x-4x - 3

1 < 4x-3

Add 3 to each side

1+3 < 4x-3+3

4 < 4x

Divide by 4

4/4 <4x/4

1 <x

Now the other

8x - 3 < 4x + 5

Subtract 4x from each side

8x -4x-3 < 4x+5-4x

4x-3 < 5

Add 3 to each side

4x-3+3 < 5+3

4x<8

Divide by 4

4x/4 <8/4

x <2

Put them back together

1 <x <2