Inequalities

Inequalities are used to articulate the connection between two expressions or values that aren't equivalent. The symbols utilized in inequalities include less than (<), greater than (>), less than or equal to (≤), and greater than or equal to (≥). The process of solving inequalities is centered around determining the spectrum of values that make the inequality true.

Solving for a Variable

4 (k - 3) \geq 6 (1 - k)

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Determining if the Point is a Solution

Graph the inequality in the coordinate plane.

x \leq - 2

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Quadratic Inequalities

The cost to produce

x

units of wire is

C = 45 x + 450

, while the revenue is

R = 70 x

. Find all intervals where the product will t least break even. elect the correct choice below and, if necessary, fill in the answer box to complete your choice.

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Rational Inequalities

For the function

h (x) = \frac{6 x}{(x + 1) (x - 2)}

, solve the following inequality.

h (x) < 0

Select the correct choice below and fill in the answer box within your choice.

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Converting from Interval to Inequality

Translate the sentence into an incquality. The sum of a number times 5 and 28 is at least 18. Use the variable

y

for the unknown number.

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Converting to Interval Notation

Translate and solve: 72 greater than

r

is less than -432 . Give your answer in interval notation. Provide your answer below:

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Rewriting as a Single Interval

Solve the compound inequality.

- 5 x \leq - 15 or 6 x - 23 \geq 19

Select the correct choice below and, if nece

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Inequalities

Solving for a Variable

Determining if the Point is a Solution

Quadratic Inequalities

Rational Inequalities

Converting from Interval to Inequality

Converting to Interval Notation

Rewriting as a Single Interval

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