solve for x -4/3x-1<7

To solve the inequality -4/3x-1 < 7, we will follow these steps:

Step 1: Multiply both sides of the inequality by -3 to eliminate the denominator and maintain the inequality direction. (Note: Changing the inequality direction is necessary when multiplying or dividing by a negative number.)
(-3) * (-4/3x-1) < (-3) * 7
4x + 3 < -21

Step 2: Simplify the expression.
4x + 3 < -21
4x < -21 - 3
4x < -24

Step 3: Divide both sides of the inequality by 4 to isolate x.
(4x)/4 < (-24)/4
x < -6

Therefore, the solution to the inequality -4/3x-1 < 7 is x < -6.