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Solve 11-5(16-7p)>=49 for p

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11-5(16-7p)>=49

Treat inequalities as equations, with one little difference. When you divide by a negative number, the direction of the inequality switches. That doesn’t actually come into play here, but is something to keep in mind.

The first step in this problem is to distribute that 5 over the 16 and -7p. The parentheses mean the 5 is multiplied by the 16 AND the -7p

11-5(16)-5(-7p)>=49

11-80+35p>=49

Remember that the – sign stays with that 5 during the multiplication and that the product of two negatives is a positive. (-5 times -7p is 35p).

Combine like terms. The 11 and the -80 are like terms. Both are just numbers with no variables:

-69+35p>=49

Move the -69 to the right by adding 69 to both sides.

-69+35p+69>=49+69

35p>=118

Now divide both sides by 35.

35p/35>=118/35

p>=118/35