Simplify $2(3x+5)-2(1-2x)$. Answer ... Given $\frac{2y}{3}-\frac{y-4}{4}\le 5$, find the largest rational value of y. Answer ...

1. Expand both brackets, taking care of the subtraction before the second bracket.

$2(3x+5)-2(1-2x)=6x+10-2+4x$

2. Collect like terms and express in the required simplified form.

$6x+10-2+4x=10x+8=2(5x+4)$

1. Clear the denominators in the inequality.

$\frac{2y}{3}-\frac{y-4}{4}\le 5$
Multiply throughout by $12$:
$8y-3(y-4)\le 60$

2. Expand, simplify and identify the largest rational value satisfying the inequality.

$8y-3y+12\le 60$
$5y\le 48$
$y\le \frac{48}{5}=9.6$
Since all rational values less than or equal to $9.6$ are allowed, there is no largest rational value less than or equal to $9.6$ unless $9.6$ itself is included. Here it is included, so the largest rational value is $\frac{48}{5}$.