Solve the inequality.

Mathematics

2 answers:

sineoko [7]3 years ago

6 0

Q+12-2q+44>0
-q+56>0
q<56

fenix001 [56]3 years ago

5 0

Answer:

q<56

Step-by-step explanation:

An inequality is an algebraic expression that consists of two members separated by an inequality. The inequality can be <, ≤,>, ≥.

Solving an inequality consists in finding the value or values that verify it.

An inequality of the first degree is an inequality in which the variable is of degree one, as in this particular case.

In this case, the resolution must first eliminate the parentheses on the left side of the inequality. For that you apply distributive property. This property expresses that the multiplication of a number by a sum is equal to the sum of the multiplications of that number by each of the addends. So you get:

q+12-2*q-2*(-22)>0

q+12-2*q+44>0

Then the terms contained in "q" must be grouped on one side of the inequality and the independent terms on the other. In this case the terms with the variable "q" will remain on the left side of the inequality. The independent terms will be grouped on the right side, remembering that to take them to the other side of the inequality the opposite operations will be used. This is:

the opposite operation of the sum is the subtraction .
the opposite operation of subtraction is the sum .
the opposite operation of multiplication is division .
the opposite operation of the division is multiplication.

So:

q-2q>-12-44

Solving the corresponding addition and subtraction operations you get:

(-1)*q>-56

Since the coefficient that accompanies "q" is negative, it is multiplied by −1 on both sides of the inequality, so the direction of inequality will change.

q<56

Finally, the values for which the inequality is valid are those in which q is less than 56

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The latest online craze is a new game, Khan on Seven. You get 100100100 points for playing the game. In addition, you get 505050

goblinko [34]

Answer:

$50w+100 \ge 18000$

Step-by-step explanation:

Each seven-letter word is worth 50 points. $w$ words are then worth $w\times50=50w$ .

Since Sal gets 100 points for playing the game, his points total after $w$ words is $50w +100$ . If he wants to break the record, he must get, at least, 18000 points. "At least" in inequality means $\ge$ (just as "at most" means $\le$ ). Then the required inequality is

$50w+100 \ge 18000$ .

Note that the question says "18000 or more", which is why we used the $\ge$ symbol. If the phrase had been "more than 18000", we would have used $>$ .