Question

error analysis. the solution shown for the equation is incorrect. what is the correct solution? what is the error? \\(-7(5 - r) = 21\\) \\(-35 - 7r = 21\\) \\(-7r = 56\\) \\(r = -8\\) the solution is \\(\square\\). (type the value of r.)

Explanation:

Step1: Distribute -7 correctly

To solve \(-7(5 - r) = 21\), we first use the distributive property \(a(b - c)=ab - ac\). Here, \(a=-7\), \(b = 5\) and \(c=r\), so we get \(-7\times5-(-7)\times r=21\), which simplifies to \(-35 + 7r=21\).

Step2: Add 35 to both sides

Add 35 to each side of the equation \(-35 + 7r=21\). So, \(-35+35 + 7r=21 + 35\), which gives \(7r=56\).

Step3: Divide by 7

Divide both sides of the equation \(7r = 56\) by 7. We have \(\frac{7r}{7}=\frac{56}{7}\), so \(r = 8\).

The error in the original solution was in the distribution of \(-7\) over \((5 - r)\). They incorrectly wrote \(-35-7r\) instead of \(-35 + 7r\) (they forgot that multiplying \(-7\) by \(-r\) gives \(+7r\), not \(-7r\)).

Answer:

8