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

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

Determining if the Point is a Solution

Graph the inequality in the coordinate plane. \[ x \leq-2 \]

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.

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.

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.

Converting to Interval Notation

Translate and solve: 72 greater than $\mathrm{r}$ is less than -432 . Give your answer in interval notation. Provide your answer below:

Rewriting as a Single Interval

Solve the compound inequality. \[ -5 x \leq-15 \text { or } 6 x-23 \geq 19 \] Select the correct choice below and, if nece