Question

1. solve for y. 6(y - 4) ≤ 6(2y + 3)

Explanation:

Step1: Expand both sides

$6(y - 4)=6y-24$ and $6(2y + 3)=12y+18$. So the inequality becomes $6y - 24\leqslant12y+18$.

Step2: Move terms with y to one - side

Subtract $6y$ from both sides: $6y-6y - 24\leqslant12y-6y + 18$, which simplifies to $-24\leqslant6y + 18$.

Step3: Isolate the term with y

Subtract 18 from both sides: $-24-18\leqslant6y+18 - 18$, resulting in $-42\leqslant6y$.

Step4: Solve for y

Divide both sides by 6: $\frac{-42}{6}\leqslant\frac{6y}{6}$, so $y\geqslant - 7$.

Answer:

$y\geqslant - 7$