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37 votes
37 votes
Solve the inequality 4x ( 4 - x ) > 7​

User William Casarin
by
3.1k points

2 Answers

21 votes
21 votes

Answer:

1/2 < x < 7/2

Explanation:

First, simplify then put everything on one side: 16x -4x^2 -7 > 0

Then use the quadratic formula to factor and find out x.

For a quadratic equation in the form of ax^2 + bx + c = 0, use this formula:

X (1,2) = (-b ± √(b^2 -4ac))/2a

(The X (1,2) part means that there are 2 solutions for x)

In this case, a is -4, b is 16, and c is -7. By using this formula, you get that x=1/2, x=7/2

User Csotelo
by
3.1k points
17 votes
17 votes

Answer:

First, subtract

7

from each side of the inequality to isolate the

x

term while keeping the inequality balanced:

1

4

x

+

7

7

>

0

7

1

4

x

+

0

>

7

1

4

x

>

7

Now, multiply each side of the inequality by

4

to solve for

x

while keeping the inequality balanced:

4

×

1

4

x

>

4

×

7

4

4

x

>

28

1

x

>

28

x

>

28

User Andrei Aulaska
by
2.1k points