Question

Question 1
Two equations are shown.
Equation 1:
a2 = 64
Equation 2: b3 = 64
Explain why the value of a is different than the value of b using written sentences and math calculations.
/3 points



Question 2
An equation is shown:
9(3x-16)+15=6x-24
Part A: Show or explain the calculations you use to solve the equation.
/4 points

Answer 1

Question 1
a^2 = 64 and b^3 = 64.

Solve a^2 = 64: a = ±√64 = ±8. Both 8 and −8 work because 8^2 = 64 and (−8)^2 = 64.
Solve b^3 = 64: b = ∛64 = 4. Only 4 works because 4^3 = 64 while (−4)^3 = −64.

Why they differ: an even exponent (2) loses sign information, so a can be positive or negative; an odd exponent (3) preserves sign, so b has a single real value.

Question 2
Solve 9(3x − 16) + 15 = 6x − 24.

Step 1 — distribute: 9·3x = 27x and 9·(−16) = −144,
so 27x − 144 + 15 = 6x − 24.

Step 2 — combine like terms on left: −144 + 15 = −129,
so 27x − 129 = 6x − 24.

Step 3 — subtract 6x from both sides: 21x − 129 = −24.

Step 4 — add 129 to both sides: 21x = 105.

Step 5 — divide by 21: x = 105/21 = 5.

Check: left = 9(3·5 −16)+15 = 9(15−16)+15 = 9(−1)+15 = 6; right = 6·5 −24 = 6. So x = 5.