Question

1. a student was asked to solve the equation $5(6x - 1) - 4(3 - 4x) = 6$. their work is shown below.

step	work
step 1 (distribution):	$30x - 5 - 12 - 16x = 6$
step 2 (combine x - terms):	$14x - 17 = 6$
step 3 (isolate x - term):	$14x = 23$
step 4 (solve):	$x = \frac{23}{14}$

in which step did the student make the first error?

a) step 1: the student incorrectly distributed the negative sign.

b) step 2: the student incorrectly combined the x - terms ($30x$ and $-16x$).

c) step 3: the student incorrectly isolated the x - term ($-17$ to $23$).

d) step 4: the calculation of the final answer is incorrect.

Explanation:

Step1: Analyze Step 1

The original equation is \(5(6x - 1)-4(3 - 4x)=6\). When distributing \(-4\) to \((3 - 4x)\), we should get \(-4\times3+(-4)\times(-4x)=-12 + 16x\), but the student wrote \(-12-16x\). So there's a sign error in distribution.

Step2: Check other steps (optional, but to confirm)

• Step 2: If Step 1 had correct distribution (\(30x - 5-12 + 16x\)), combining \(x\)-terms would be \(46x-17\), but since Step 1 is wrong, we focus on Step 1 first.
• Step 3 and 4: Depend on previous steps, so the first error is in Step 1.

Answer:

a) Step 1: The student incorrectly distributed the negative sign.