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

To solve the first inequality, we need to simplify both sides of the equation and isolate the variable x.

5(x + 1) ≤ 3(x + 3) + 1

First, distribute on both sides:

5x + 5 ≤ 3x + 9 + 1

Combine like terms:

5x + 5 ≤ 3x + 10

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

5x - 3x + 5 ≤ 3x - 3x + 10

This simplifies to:

2x + 5 ≤ 10

Now, subtract 5 from both sides:

2x + 5 - 5 ≤ 10 - 5

This simplifies to:

2x ≤ 5

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

2x/2 ≤ 5/2

This simplifies to:

x ≤ 2.5

Therefore, the solution to the inequality is x ≤ 2.5.

Now let's solve the second inequality:

2x - 1/7 ≤ x + 1/2

First, let's get rid of the fractions by finding a common denominator. The common denominator is 14.

Multiplying all terms by 14:

14(2x - 1/7) ≤ 14(x + 1/2)

This simplifies to:

28x - 2 ≤ 14x + 7

Next, subtract 14x from both sides:

28x - 14x - 2 ≤ 14x - 14x + 7

This simplifies to:

14x - 2 ≤ 7

Now, add 2 to both sides:

14x - 2 + 2 ≤ 7 + 2

This simplifies to:

14x ≤ 9

Finally, divide both sides by 14 to solve for x:

14x/14 ≤ 9/14

This simplifies to:

x ≤ 0.64

Therefore, the solution to the second inequality is x ≤ 0.64.