Prove that if ||u||=||v||, then (u+v)·(u−v) = 0.

Solve the equations
(a)${\displaystyle x-2=4-x}$ and ${\displaystyle x-2>4-x}$
(b)${\displaystyle -2x+3=3x-7}$ and ${\displaystyle -2x+3\le 3x-7}$

Last Saturday, 1,750 people attended an event at Farway Gardens. The admission fee was $3.50 for children and $8.00 for adults. If the total amount of money collected at the event was $9,860, how many children and how many adults attended the event?

Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation.
$3x(x-1)=x+6$

Solve the following equations and inequalities:
1) ${\displaystyle -x^2+2x>1}$
2) ${\displaystyle |1-3x|=5}$
3) ${\displaystyle |4x-3|\le 2}$

Which of the pairs satisfy the inequality ${\displaystyle 2x-3y<5}$?
a) ${\displaystyle (2,0)}$
b) ${\displaystyle (1,-1)}$
c) ${\displaystyle (0,0)}$
d) ${\displaystyle (2,4)}$

How do I interpret this equation $5+1\times 10=$ is the answer 15 or 60?

solve each problem by setting up and solving an appropriate system of equations. In a class of 50 students, the number of females is two more than five times the number of males. How many females are there in the class?