Question

expressions-polynomials-linear expressions:
(1 point)
answer each of the following questions by t (for true) or f (for false).
if you answer true you are saying that the equation is true for all values of a, b, and c.
if you find working with letters confusing you can test your ideas by letting a = 3, b = 4, and c = 5.

i) (a + b) + c = a + (b + c) is

ii) (a - b) - c = a - (b - c) is

iii) (a - b) + c = a - (b + c) is

iv) (a + b) - c = a + (b - c) is

v) (a ÷ b) ÷ c = a ÷ (b ÷ c) is

vi) (a ÷ b) × c = a ÷ (b × c) is

vii) (a × b) ÷ c = a × (b ÷ c) is

viii) (a × b) × c = a × (b × c) is

Explanation:

i)

Step1: Recall the associative property of addition

The associative property of addition states that for any real numbers \(a\), \(b\), and \(c\), \((a + b)+c=a+(b + c)\).

Step2: Verify with \(a = 3\), \(b = 4\), \(c = 5\)

Left - hand side: \((3 + 4)+5=7 + 5=12\)
Right - hand side: \(3+(4 + 5)=3 + 9=12\)
Since LHS = RHS for \(a = 3\), \(b = 4\), \(c = 5\) and the property holds for all real numbers, the statement is true.

Step1: Simplify both sides

Left - hand side: \((a - b)-c=a - b - c\)
Right - hand side: \(a-(b - c)=a - b + c\)

Step2: Verify with \(a = 3\), \(b = 4\), \(c = 5\)

Left - hand side: \((3-4)-5=-1 - 5=-6\)
Right - hand side: \(3-(4 - 5)=3-(-1)=3 + 1 = 4\)
Since \(-6
eq4\), the statement is false.

Step1: Simplify both sides

Left - hand side: \((a - b)+c=a - b + c\)
Right - hand side: \(a-(b + c)=a - b - c\)

Step2: Verify with \(a = 3\), \(b = 4\), \(c = 5\)

Left - hand side: \((3-4)+5=-1 + 5 = 4\)
Right - hand side: \(3-(4 + 5)=3-9=-6\)
Since \(4
eq - 6\), the statement is false.

Answer:

T

ii)