Solve the compound inequality
-16≤3x-4<2
To solve the compound inequality, we will solve each inequality separately and then find the values that satisfy both inequalities.
First, let's solve the inequality 3x - 4 < 2:
Add 4 to both sides: 3x - 4 + 4 < 2 + 4
Simplify: 3x < 6
Divide both sides by 3: (3x)/3 < 6/3
Simplify: x < 2
Now let's solve the inequality -16 ≤ 3x - 4:
Add 4 to both sides: -16 + 4 ≤ 3x - 4 + 4
Simplify: -12 ≤ 3x
Divide both sides by 3: (-12)/3 ≤ (3x)/3
Simplify: -4 ≤ x
So, we have x < 2 and -4 ≤ x as the two separate inequalities.
To find the values that satisfy both inequalities, we need to find the intersection of the two solution sets.
Since -4 is less than 2, the values that satisfy both inequalities are x values between -4 and 2, including -4 but not including 2.
Therefore, the solution to the compound inequality -16 ≤ 3x - 4 < 2 is -4 ≤ x < 2.