Final answer:
The smallest integer that satisfies the inequality -2/3x - 4 < 6 is -14. This is found by isolating the variable x and determining the least integer greater than the resulting value.
Step-by-step explanation:
To find the smallest integer that satisfies the inequality -2/3x - 4 < 6, we must first isolate the variable x. We do this by adding 4 to both sides of the inequality, which gives us:
-2/3x < 10
To remove the fraction, we can multiply both sides by -3/2 to get x by itself. Remember that multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality sign. So, now we have:
x > -15
The next step is to find the smallest integer greater than -15, which is -14. Therefore, -14 is the smallest integer that satisfies the given inequality.