Question

you be the teacher your friend solves the equation. is your fr
-2(7 - y)+4=-4
-14 - 2y + 4=-4
-10 - 2y=-4
-2y = 6
y=-3
yes
no
explain your reasoning.

Explanation:

Step1: Expand the left - hand side of the equation

Use the distributive property \(a(b - c)=ab - ac\). For \(-2(7 - y)+4\), we have \(-2\times7-2\times(-y)+4=-14 + 2y+4\). The friend made a mistake in the sign when distributing \(-2\) to \(-y\). It should be \(-14 + 2y+4\) instead of \(-14-2y + 4\).

Step2: Simplify the left - hand side

Combine like terms: \(-14 + 2y+4=2y-10\). So the equation becomes \(2y-10=-4\).

Step3: Solve for \(y\)

Add \(10\) to both sides of the equation: \(2y-10 + 10=-4 + 10\), which gives \(2y = 6\). Then divide both sides by \(2\): \(y=\frac{6}{2}=3\).

Answer:

no. The friend made a sign error when distributing \(-2\) to \(-y\) in the step \(-2(7 - y)+4=-14-2y + 4\). The correct distribution is \(-2(7 - y)+4=-14 + 2y+4\), and the correct solution is \(y = 3\).