The work of a student to solve the equation 4(3x − 4) = 8 + 4x + 8 is shown below: Step 1. 4(3x − 4) = 8 + 4x + 8 Step 2. 7x − 8 = 16 + 4x Step 3. 7x − 4x = 16 + 8 Step 4. 3x = 24 Step 5. x = 8 In which step did the student first make an error and what is the correct step? (1 point) a Step 2, 12x − 16 = 16 + 4x b Step 2, 12x − 8 = 2(4 + 2x + 4) c Step 3, 7x − 4x = 16 − 8 d Step 3, 7x + 4x = 16 + 8

wrong

Step-by-step explanation:

the student added 4x with 3 instead of multiplying

 Step 2, and correct would be a) Step 2, 12x − 16 = 16 + 4x

Step-by-step explanation:

Step 1. 4(3x − 4) = 8 + 4x + 8

Step 2. 7x − 8 = 16 + 4x

Step 3. 7x − 4x = 16 + 8

Step 4. 3x = 24

Step 5. x = 8

The student first make an error in Step 2, it should be 4 multiply the number inside the parentheses, which would be 4(3x) + 4(-4) = 8 + 4x + 8. We get 12x - 16 = 16 + 4x, which is choice a.

step-by-step explanation:

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.