Translate the sentence into an inequality?

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2 Answers
Feb 18, 2018

2c - 6 <= -25

Explanation:

Since we are using the variable c, we have to determine what c's relationship to the other numbers is.

Since the question says twice the difference of a number and 6, and c is "a number", we know that we should use 2c - 6 on one side of the inequality. The other side should be "at least -25", which means -25 is on the right, and the inequality should be -25 or greater. Another way to put it is that the 2c - 6 should be less or equal to -25.

Now if we make this an inequality, it becomes:

2c - 6 <= -25

If you want to solve:

2c - 6 <= -25
2c - 6 +6 <= -25+6
2c <= -19
c <= -9.5

Feb 18, 2018

2abs(c-6) >= -25

Explanation:

Twice color(blue)("the difference of a number and 6") is at least -25
rarr Twice color(blue)(abs(c-6)) is at least -25

color(magenta)("Twice ")color(blue)(abs(c-6)) is at least -25
rarr color(magenta)2color(blue)(abs(c-6)) is at least -25

color(magenta)2color(blue)(abs(c-6))color(orange)(" is at least ") -25
rarr color(magenta)2color(blue)(abs(c-6))color(orange)(>=)-25

Notice that this will be true for all Real values of c,
so it might be that color(blue)("the difference of a number and 6") was intended to be translated as either color(blue)(""(c-6)) or as color(blue)(""(6-c))