4×2+4y2-24x+8x<-39

Add -24x and 8x.

4×2+4y2-16x<-39

Move all terms not containing y to the right side of the inequality.

Subtract 4×2 from both sides of the inequality.

4y2-16x<-39-4×2

Add 16x to both sides of the inequality.

4y2<-39-4×2+16x

4y2<-39-4×2+16x

Divide each term by 4 and simplify.

Divide each term in 4y2<-39-4×2+16x by 4.

4y24<-394+-4×24+16×4

Cancel the common factor of 4.

Cancel the common factor.

4y24<-394+-4×24+16×4

Divide y2 by 1.

y2<-394+-4×24+16×4

y2<-394+-4×24+16×4

Simplify each term.

Move the negative in front of the fraction.

y2<-394+-4×24+16×4

Cancel the common factor of -4 and 4.

Factor 4 out of -4×2.

y2<-394+4(-x2)4+16×4

Cancel the common factors.

Factor 4 out of 4.

y2<-394+4(-x2)4(1)+16×4

Cancel the common factor.

y2<-394+4(-x2)4⋅1+16×4

Rewrite the expression.

y2<-394+-x21+16×4

Divide -x2 by 1.

y2<-394-x2+16×4

y2<-394-x2+16×4

y2<-394-x2+16×4

Cancel the common factor of 16 and 4.

Factor 4 out of 16x.

y2<-394-x2+4(4x)4

Cancel the common factors.

Factor 4 out of 4.

y2<-394-x2+4(4x)4(1)

Cancel the common factor.

y2<-394-x2+4(4x)4⋅1

Rewrite the expression.

y2<-394-x2+4×1

Divide 4x by 1.

y2<-394-x2+4x

y2<-394-x2+4x

y2<-394-x2+4x

y2<-394-x2+4x

y2<-394-x2+4x

Take the square root of both sides of the inequality to eliminate the exponent on the left side.

y<±-394-x2+4x

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Let u=-1. Substitute u for all occurrences of -1.

Apply the distributive property.

y<±u⋅39+u(4×2)+4x⋅44

Move 39 to the left of u.

y<±39⋅u+u(4×2)+4x⋅44

Rewrite using the commutative property of multiplication.

y<±39⋅u+4ux2+4x⋅44

Multiply 4 by 4.

y<±39u+4ux2+16×4

y<±39u+4ux2+16×4

Replace all occurrences of u with -1.

y<±39⋅-1+4⋅(-1×2)+16×4

Simplify each term.

Multiply 39 by -1.

y<±-39+4⋅(-1×2)+16×4

Multiply 4 by -1.

y<±-39-4×2+16×4

y<±-39-4×2+16×4

Reorder terms.

y<±-4×2+16x-394

Rewrite -4×2+16x-394 as (12)2(-4×2+16x-39).

Factor the perfect power 12 out of -4×2+16x-39.

y<±12(-4×2+16x-39)4

Factor the perfect power 22 out of 4.

y<±12(-4×2+16x-39)22⋅1

Rearrange the fraction 12(-4×2+16x-39)22⋅1.

y<±(12)2(-4×2+16x-39)

y<±(12)2(-4×2+16x-39)

Pull terms out from under the radical.

y<±12⋅-4×2+16x-39

Combine 12 and -4×2+16x-39.

y<±-4×2+16x-392

y<±-4×2+16x-392

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

y<-4×2+16x-392

Next, use the negative value of the ± to find the second solution. Since this is an inequality, flip the direction of the inequality sign on the – portion of the solution.

y>–4×2+16x-392

The complete solution is the result of both the positive and negative portions of the solution.

y<-4×2+16x-392 and y>–4×2+16x-392

Find the intersection.

–4×2+16x-392<y<-4×2+16x-392

–4×2+16x-392<y<-4×2+16x-392

–4×2+16x-392<y<-4×2+16x-392

–4×2+16x-392<y<-4×2+16x-392

The equation is not linear, so the slope does not exist.

Not Linear

Graph a dashed line, then shade the area below the boundary line since y is less than .

–4×2+16x-392<y<-4×2+16x-392

<div data-graph-input="{"graphs":[{"ascii":"-(\sqrt(-4x^(2)+16x-39))/(2)<y