#### Answer

The solution is $(-\infty,1]\cup\Big(\dfrac{29}{7},\infty\Big)$

#### Work Step by Step

$3x+2\le5$ or $7x\gt29$
Solve the first inequality:
$3x+2\le5$
Take $2$ to the right side:
$3x\le5-2$
$3x\le3$
Take $3$ to divide the right side:
$x\le\dfrac{3}{3}$
$x\le1$
Expressing the solution in interval notation:
$(-\infty,1]$
Solve the second inequality:
$7x\gt29$
Take $7$ to divide the right side:
$x\gt\dfrac{29}{7}$
Expressing the solution in interval notation:
$\Big(\dfrac{29}{7},\infty\Big)$
Since the compound inequality is formed by the word "or", the solution is composed by the solutions of both inequalities:
The solution is $(-\infty,1]\cup\Big(\dfrac{29}{7},\infty\Big)$