(4x+6)< 2(5x+9)+2x write the solution for interval notation

Step-by-step explanation:

-(4x+6)<2(5x+9)+2x

Distribute:

-4x-6<10x+18+2x

Combine like terms on either side:

-4x-6<12x+18

We want to now gather variable terms on one side of the inequality and constants (terms without variables) on the opposing side.

Add 4x on both sides:

-6<16x+18

Subtract 18 on both sides:

-24<16x

Divide both sides by 16:

-24/16<x

This implies:

x>-24/16

Reduce:

x>-3/2

x>-1.5

So in an interval notation this is .

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).