Question

Can you guys please help me solve these

Answer 1

See explanation below

Explanation:

In all cases you need to isolate x on one side of the inequality symbol using inverse operations.

1.-

`15+x\leq -45\\15-15+x\leq -45-15\\x\leq -60`

where we subtracted from both side 15 in order to leave x by itself on the left.

2.-

`x-14>12\\x-14+14>12+14\\x>26`

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 > )

`-5x<35\\(-5\,x)/(-5) >(35)/(-5) \\x>-7`

4.-

`2x>-42\\(2\,x)/(2) >(-42)/(2) \\x>-21`

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)