[tex]-3-4x\leq 21 \\~\\-3-4x+3\leq 21+3 \\~\\-4x \leq 24[/tex]
When you multiply both sides by a negative number, you have to flip the inequality.
[tex]-4x\cdot \left(-\dfrac{1}{4}\right) \geq24\cdot \left(-\dfrac{1}{4}\right) \\~\\x \geq-6[/tex]
You could also solve by doing this:
[tex]-4x \leq 24 \\~\\-4x +(4x-24) \leq 24 +(4x-24) \\~\\-24 \leq 4x \\~\\-6\leq x[/tex]
If -6 is less than or equal to x, then x is greather than or equal to -6.
