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Solve \(\displaystyle | 9 x + 1 | \geq 28\)
The inequality is an "or" type compound inequality. This gives the two inequalities \(\displaystyle 9 x + 1 \leq -28\) or \(\displaystyle 9 x + 1 \geq 28\). Solving gives \(\displaystyle 9 x \leq -29\) or \(\displaystyle 9 x \geq 27\). Isolating \(\displaystyle x\) gives \(\displaystyle x \leq - \frac{29}{9}\) or \(\displaystyle x \geq 3\).
\begin{question}Solve $| 9 x + 1 | \geq 28$
\soln{9cm}{The inequality is an "or" type compound inequality. This gives the two inequalities $9 x + 1 \leq -28$ or $9 x + 1 \geq 28$. Solving gives $9 x \leq -29$ or $9 x \geq 27$. Isolating $x$ gives $x \leq - \frac{29}{9}$ or $x \geq 3$. }
\end{question}
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\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Solve <img class="equation_image" title=" \displaystyle | 9 x + 1 | \geq 28 " src="/equation_images/%20%5Cdisplaystyle%20%7C%209%20x%20%2B%201%20%7C%20%5Cgeq%2028%20" alt="LaTeX: \displaystyle | 9 x + 1 | \geq 28 " data-equation-content=" \displaystyle | 9 x + 1 | \geq 28 " /> </p> </p>
<p> <p>The inequality is an "or" type compound inequality. This gives the two inequalities <img class="equation_image" title=" \displaystyle 9 x + 1 \leq -28 " src="/equation_images/%20%5Cdisplaystyle%209%20x%20%2B%201%20%5Cleq%20-28%20" alt="LaTeX: \displaystyle 9 x + 1 \leq -28 " data-equation-content=" \displaystyle 9 x + 1 \leq -28 " /> or <img class="equation_image" title=" \displaystyle 9 x + 1 \geq 28 " src="/equation_images/%20%5Cdisplaystyle%209%20x%20%2B%201%20%5Cgeq%2028%20" alt="LaTeX: \displaystyle 9 x + 1 \geq 28 " data-equation-content=" \displaystyle 9 x + 1 \geq 28 " /> . Solving gives <img class="equation_image" title=" \displaystyle 9 x \leq -29 " src="/equation_images/%20%5Cdisplaystyle%209%20x%20%5Cleq%20-29%20" alt="LaTeX: \displaystyle 9 x \leq -29 " data-equation-content=" \displaystyle 9 x \leq -29 " /> or <img class="equation_image" title=" \displaystyle 9 x \geq 27 " src="/equation_images/%20%5Cdisplaystyle%209%20x%20%5Cgeq%2027%20" alt="LaTeX: \displaystyle 9 x \geq 27 " data-equation-content=" \displaystyle 9 x \geq 27 " /> . Isolating <img class="equation_image" title=" \displaystyle x " src="/equation_images/%20%5Cdisplaystyle%20x%20" alt="LaTeX: \displaystyle x " data-equation-content=" \displaystyle x " /> gives <img class="equation_image" title=" \displaystyle x \leq - \frac{29}{9} " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cleq%20-%20%5Cfrac%7B29%7D%7B9%7D%20" alt="LaTeX: \displaystyle x \leq - \frac{29}{9} " data-equation-content=" \displaystyle x \leq - \frac{29}{9} " /> or <img class="equation_image" title=" \displaystyle x \geq 3 " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cgeq%203%20" alt="LaTeX: \displaystyle x \geq 3 " data-equation-content=" \displaystyle x \geq 3 " /> . </p> </p>