What is the solution of 9|2x – 1| + 4 < 49?

2 answers:

Aneli [31]2 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

Given

9 | 2x - 1 | + 4 < 49 ( subtract 4 from both sides )

9 | 2x - 1 | < 45 ( divide both sides by 9 )

| 2x - 1 | < 5

Inequalities of the type | x | < a always have solutions of the form

- a < x < a, thus

- 5 < 2x - 1 < 5 ( add 1 to all 3 intervals )

- 4 < 2x < 6 ( divide all 3 intervals by 2 )

- 2 < x < 3

3 0

Answer: $-2$

Step-by-step explanation:

You need to set up two cases (Positive case and negative case) and solve for "x".

- POSITIVE CASE IF: $2x-1>0$

$9(2x -1) + 4 < 49\\18x-9$

- NEGATIVE CASE IF: $2x-1$

$-9(2x -1) + 4 < 49\\-18x+9$

Therefore, the solution is:

$-2$

You might be interested in

lara [203]

Huhvffghgcddtujgffyjbfghj

7 0

2 years ago

KATRIN_1 [288]

Answer:

If the perimeter of a square measures 32 cm, each side measures 32/4= 8 cm, because all sides are equal.
The diagonal that passes through the center of the square divides the square into two triangles. The triangles are formed by a hypotenuse (the diagonal, which is k in this case), and two sides, that measure 8 cm each, in this case.
Because of Pythagoras' theorem, we know that the lenght of the hypotenuse (in this case the hypotenuse is k) equals the squared root of the sum of the squared sides, which in this case can be expressed as $k=\sqrt{8^2+8^2} =\sqrt{64+64}=\sqrt{128}=11.31$ .
Then, k=11.31 cm.