Please help with this no fakes

9514 1404 393

  h ≤ -7/2

Step-by-step explanation:

This is what is known as a "2-step" problem.

The first step is to "isolate the variable term" by adding the opposite of the term on the left that does not have the variable in it. That is, we want to add -4 to both sides of the inequality.

  4 -4 +2h ≤ -3 -4 . . . . add -4 to both sides

  2h ≤ -7 . . . . . . . . . . variable term isolated

Now, we want to get rid of the coefficient of the variable (make it be 1), so we use the multiplicative inverse. That is, we multiply both sides of the inequality by 1/2, the reciprocal of the coefficient.

  (1/2)(2h) ≤ (1/2)(-7) . . . . . multiply both sides by 1/2

  h ≤ -7/2 . . . . the solution

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For an inequality, multiplying or dividing by a negative number causes the direction of the comparison to be reversed. (Here, our multiplier was 1/2, not negative, so no such reversal was required.)

Example:

  1 < 2

  -1 > -2 . . . . . both sides multiplied (or divided) by -1

Additional comment

As when solving equations, you must do the same thing to both sides of the inequality.

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