All categories

3 years ago

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

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

3 0

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

You might be interested in

Which expression is the best estimate of the product of 7/8 and 8 1/10

gtnhenbr [62]

Answer:

Step-by-step explanation:

i don't see options to select from but my guess would be 8 because 7/8 is very close to being one and 8 1/10 is close to 8; 8 x 1 = 8

4 0

3 years ago

Find the temperature that is 12°C<br> lower than 6°C

aleksandrvk [35]

Answer:

-6°C

Step-by-step explanation:

12 lower than 6.

$6-12\\=-6$

6 0

3 years ago

1. Emmanuel bought 28 lb of potting soil this week. This amount is 4 lb more than twice the amount of potting soil he bought las

Cerrena [4.2K]

The answer would be 58 lb.

3 0

3 years ago

Read 2 more answers

Mercury orbits the sun in 87 24/25 Earth days. Venus orbits the sun in 224 7/10 Earth days, and Mars orbits the sun in 686 49/50

kompoz [17]

mercury 2,199 = 24 + 25 × 87 and divide 2,199/25
= 87.96

Venus (2,240 + 7 )/10 = 224.7

Mars = 686.98

8 0

3 years ago

The length of a leg of an isosceles right triangle is 20 inches. Find the length of the hypotenuse in radical form

Over [174]

Answer: H = 20 $\sqrt{2}$

Step-by-step explanation:

To find the hypotenuse , we will use Pythagoras theorem, which states that

The square of the hypotenuse = the square of the adjacent + the square of the opposite.

Since , we are dealing with isosceles right triangle , this means that :

both the adjacent and the opposite are equal, using the formula to find the hypotenuse , let H represent the hypotenuse , then

$H^{2}$ = $20^{2}$ + $20^{2}$

$H^{2}$ = 400 + 400

$H^{2}$ = 800

Take the square root of both sides

H = $\sqrt{800}$

$\sqrt{800}$ can be written as $\sqrt{400}$ x $\sqrt{2}$

Therefore :

H = $\sqrt{400}$ x $\sqrt{2}$

H = 20x $\sqrt{2}$

H = 20 $\sqrt{2}$

6 0

3 years ago