Math Please help!?!?!?

Question

Solve each inequality by sketching on a number line 

4x2<10x-1 

Graph the following 
10x-4y+3<11 
y>=x2-3x-4 

Answer 1

2) The system 10x - 4y + 3 < 11 and y >= x^2 - 3x - 4 .

First inequality 10x - 4y - 8 < 0

Second inequality y >= x^2 - 3x - 4

To solve the inequality system first graph the system.

The fact that these expressions are inequalities and not equations doesn’t change the general shape of the graph at all.

Therefore, you can graph these inequalities just as you would graph them if they were equations.

First inequality 10x - 4y - 8 < 0

1) draw the coordinate plane.Graph te line y = (5/2)x - 2.

2) Since the inequality 10x -4y - 8 < 0 The symbol is < ,the boundary is not included in the solution set.

Graph the boundary of inequality 10x - 4y - 8 < 0 with dotted line.

3) To determine which half - plane to be shaded use a test point in either half plne.

A simple choice is (0,0),substitute x = 0, y = 0 in original inequality 10x - 4y -8 < 0.

-8 < 0

The statement is true.

4) since the statement is true ,shade the region contains point (0,0) in aqua colour.

Second inequality y >= x^2 - 3x - 4

5) Since the inequality y >= x^2 - 3x - 4Symbol is >=,the boundary is included in the solution set.

Graph the boundary of the inequality y >= x^2 - 3x - 4 with solid line.

A simple choice is (2, 3)

Substitute x = 2, y = 3 in original inequality y >= x^2 - 3x - 4

3 > = -12

The statement is true.

Since the statement is true, the graph will be shaded inside the parabola.shaded in fuchsia colour.

Graph

The solution of the system is the set of ordered pairs in the intersection of the graph of

10x - 4y - 8 < 0 and y >= x^2 - 3x - 4 .

This region is shaded in light purple color.

Answer 2

1) The inequality 4x ² < 10x - 1

4x ² -10x +1 < 0   

Now solve the equation

Compare it to quadratic form

Roots are

x = (5 + 4.58)/4 and x = (5 - 4.58)/4

x = 9.58/4 and x = 0.417/4

x  = 2.39 and x  = 0.104

So the solution of the inequality is 0.104 <  x  < 2.39.

Solution on number line