Isolate the variable x from the formulaformulaformula.

a) $3x+2=x-a$

b) $1-x=1-2a$

c) $-4x+y+5=5y$

Isolate the given variable from the formulaformulaformula. Give necessary assumptions.

a) $I=\frac{U}{R},$ isolate R

b) $F=m\cdot a,$ isolate m

c) $s=\frac{a·t^2}{2},$ isolate a

d) $\frac{T_1}{v_1}=\frac{T_2}{v_2},$ isolate TIndeks dolny 1₁

Area of a triangle whose base is 2a is equal to $\frac{1}{5}a$. Determine the altitude of this triangle.

An extra task:

From the following formulas isolate given variable. All variables are positive numbers.

a) $\frac{x}{y}=\frac{z}{v},$ isolate z and v

b) $\frac{2x}{y}=\frac{5z}{3},$ isolate x and z

c) $\frac{x+2}{3y}=\frac{2}{3v},$ isolate y and z

Give formula for the perimeter of $a$ rectangle whose sides are $a$ and $b$ isolate the length of $b$ from this formula.

Look for information in the Internet about the most famous formula discovered by a brilliant mathematician Albert Einstein – the relativity theory. Isolate any chosen value from this formula. Describe the solution in English.