Solve for x.

5(x − 3) − 6(x − 2) > 8x + 2
Responses
A x > 59
x > 5 9
B x < 5/9
x < 5 9
C x > −5/9
x > − 5 9
D x < −5/9
x < − 5 9
E x > −9/5

1 answer

To solve the inequality, we first simplify both sides:

5(x - 3) - 6(x - 2) > 8x + 2
5x - 15 - 6x + 12 > 8x + 2
-x - 3 > 8x + 2

Next, we want to isolate the variable, so we'll combine like terms:

-7x - 3 > 8x + 2

Now, we'll move the variable terms to one side and the constant terms to the other side:

-7x - 8x > 2 + 3
-15x > 5

To solve for x, we need to divide both sides by -15. However, we must be careful because we are dividing by a negative number. This means that the inequality sign will flip.

x < 5/15

Simplifying the right side gives:

x < 1/3

So the solution to the inequality is x < 1/3.

The correct answer is B. x < 5/9.