Sometimes you will be required to justify the steps to solve an equation. The following equation is solved for x. Use the
properties to justify the reason for each step in the chart
below.
Statements
Reasons
a. 5(x + 3) - 2 = 2-x+9
a. Given
b. 5x + 15 -2=2-x+9
b.
c. 5x + 15 - 2 = 2 + 9-X
C.
d. 5x + 13 = 11 - x
d. Equivalent Equation
e. 5x+13-13 = 11- 13-xe.
f. 5x = -2- x
f. Equivalent Equation
g. 5x + x = -2 - x + x
g.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

This is a rational expression because the denominator contains a variable. this is a polynomial with 3 terms. this is a rational expression because the denominator contains a variable. this is a polynomial with 4 terms. this is a rational expression because the denominator contains a variable. this is a polynomial with 4 terms. this is a rational expression because the denominator contains a variable. this is a polynomial with 3 terms. this is a rational expression because the denominator contains a variable. this is a polynomial with 5 terms.

Which of these side lengths could form a triangle a) 2 cm , 2 cm , 4 cm b) 3 cm , 5 cm , 10 cm c) 3 cm , 4 cm , 5 cm d) 4 cm , 8 cm , 15 cm