Alan

Multiply both sides by 4

2.5x +1.5(x - 4) = -4x

Multiply the bracketed term by 1.5

2.5x + 1.5x - 1.5*4 = -4x

Simplify the left-hand side

4x - 6 = -4x

Add 4x to both sides

8x - 6 = 0

Add 6 to both sides

8x = 6

Divide both sides by 8

x = 6/8

Simplify

x = 3/4  (or x = 0.75)

Ok.  You can use whatever symbols you like for both son's age and father's age.  Let me use x for son's age and y for father's age then.

father (y) is now 4 times as old as son (x) is now.   y = 4x   ...(1)

5 years ago father was y-5 years old, and son was x-5 years old.  At that time father was 7 times as old as his son.

 y - 5 = 7*(x - 5)    ...(2)

Replace the y in (2) by using (1)

4x - 5 = 7*(x - 5)

4x - 5 = 7x - 35

4x - 5 + 35 = 7x 

4x +30 = 7x

4x + 30 - 4x = 7x - 4x

30 = 3x

x = 10  ...(3)

Put (3) into (1)

y = 4*10

y = 40

Is this any clearer?

Area of Beijing: A ≈ 16400km²

Take standard marble diameter: d = 5/8"

Number of marbles of 1 marble depth required to cover Beijing: N ≈ A/d² ≈ 6.5*10¹³

One mole of marbles = Avogadro's number worth of marbles; Av ≈ 6*10²³

Depth of Avogadro's number of marbles on Beijing ≈ d*Av/N ≈ 1.5*10⁵ km  

They would reach about half way to the moon!

Let f = father's age and s = son's age

f = 4*s                                 father is 4 times older than son

f - 5 = 7*(s - 5)                   5 years ago father was f -5 and son was s-5  and father was 7 times older

Replace f in 2nd equation above with 4s from first equation,

4*s - 5 = 7*s - 7*5  so that:

30 = 3*s

s = 10

f = 4*10 = 40

Rewrite as y = (9 - x²)^1/2

The slope at any point x is then given by slope = -x/(9 - x²)^1/2

When x = 2 the slope is -2/(9 - 2²)^1/2 = -2/√5

The equation of a straight line is y = m*x + c where m is the slope and c is a constant (the y-intercept).  We know the slope and can find c because we know that when x = 2, y = √5, so

√5 = (-2/√5)*2 + c

c = √5+4/√5 or c = √5*(1+4/5) 0r c = 1.8*√5

So  y = (-2/√5)*x + 1.8*√5

or y = √5*(-2/5)x + 1.8*√5

or y = -0.4*√5*x + 1.8*√5

A simple check to determine if a number is divisible by 3 is to keep adding up the digits of the number and see if the result is divisible by 3.

So:  1+7+8+6 = 22

        2 + 2 = 4

4 isn't divisible by 3, so neither is 1786.

$${\frac{{\mathtt{4}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}{\mathtt{3\,008}} = {\frac{{\mathtt{3\,008}}}{{\mathtt{25}}}} = {\mathtt{120.32}}$$

Rearrange as 

√(x + 14) = 8 - 2x

Square both sides

x + 14 = (8 - 2x)²

x + 14 = 64 - 32x + 4x²

Collect like terms

4x² - 33x + 50 = 0

$${\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{33}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{50}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\frac{{\mathtt{25}}}{{\mathtt{4}}}}\\ {\mathtt{x}} = {\mathtt{2}}\\ \end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{6.25}}\\ {\mathtt{x}} = {\mathtt{2}}\\ \end{array} \right\}$$

Check in the original equation:

$${\mathtt{LHS}} = {\sqrt{{\mathtt{6.25}}{\mathtt{\,\small\textbf+\,}}{\mathtt{14}}}} \Rightarrow {\mathtt{LHS}} = {\mathtt{4.5}}$$

$${\mathtt{RHS}} = {\mathtt{8}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{6.25}} \Rightarrow {\mathtt{RHS}} = -{\mathtt{4.5}}$$

So x ≠ 6.25

Check the other solution

$${\mathtt{LHS}} = {\sqrt{{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{14}}}} \Rightarrow {\mathtt{LHS}} = {\mathtt{4}}$$

$${\mathtt{RHS}} = {\mathtt{8}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}} \Rightarrow {\mathtt{RHS}} = {\mathtt{4}}$$

So x = 2 is the solution to the original equation.

The general equation for a sphere, centred at (0,0,0) is  x² + y² + z² = r²

Rearrange this as  z = (r² - x² - y²)^1/2    

The slope of z with respect to x is given by

∂z/∂x = -x/ (r² - x² - y²)^1/2

The slope of z with respect to y is given by

∂z/∂y = -y/ (r² - x² - y²)^1/2

You have the values of x, y and r, so I'll leave you to plug them into these formulae.