Answer:
See explanation below
Step-by-step explanation:
In all cases you need to isolate x on one side of the inequality symbol using inverse operations.
1.-
[tex]15+x\leq -45\\15-15+x\leq -45-15\\x\leq -60[/tex]
where we subtracted from both side 15 in order to leave x by itself on the left.
2.-
[tex]x-14>12\\x-14+14>12+14\\x>26[/tex]
where we added 14 in order to isolate x on the left
3.-
In this case we need to divide both sides by -5 in order to isolate the x which is being multiplied by the factor -5, but he have to recall that multiplying or dividing by a negative number changes the direction of the inequality symbol (in our case from < into > )
[tex]-5x<35\\\frac{-5\,x}{-5} >\frac{35}{-5} \\x>-7[/tex]
4.-
[tex]2x>-42\\\frac{2\,x}{2} >\frac{-42}{2} \\x>-21[/tex]
In this case we simply divide both sides by two, and there is no change in the direction of the inequality because the number we are using to divide is a positive number (2)
