5(x + 1) ≤ 3(x + 3) + 1 (2x − 1)/7 ≤ (x + 1)/2

To solve the first inequality, we can start by simplifying both sides:

5(x + 1) ≤ 3(x + 3) + 1 5x + 5 ≤ 3x + 9 + 1 5x + 5 ≤ 3x + 10

Next, we can subtract 3x from both sides to isolate the x term:

5x - 3x + 5 ≤ 3x - 3x + 10 2x + 5 ≤ 10

Now, subtract 5 from both sides to isolate the x term:

2x + 5 - 5 ≤ 10 - 5 2x ≤ 5

Finally, divide both sides by 2 to solve for x:

2x/2 ≤ 5/2 x ≤ 5/2

Therefore, the solution for the first inequality is x ≤ 5/2.

To solve the second inequality, we can start by cross-multiplying to get rid of the denominators:

2(2x - 1) ≤ 7(x + 1)

Expand the equation:

4x - 2 ≤ 7x + 7

Next, subtract 4x from both sides to isolate the x term:

4x - 4x - 2 ≤ 7x - 4x + 7 -2 ≤ 3x + 7

Now, subtract 7 from both sides:

-2 - 7 ≤ 3x + 7 - 7 -9 ≤ 3x

Finally, divide both sides by 3 to solve for x:

-9/3 ≤ 3x/3 -3 ≤ x

Therefore, the solution for the second inequality is x ≥ -3.