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Solve \(\displaystyle | 4 x - 2 | \geq 38\)
The inequality is an "or" type compound inequality. This gives the two inequalities \(\displaystyle 4 x - 2 \leq -38\) or \(\displaystyle 4 x - 2 \geq 38\). Solving gives \(\displaystyle 4 x \leq -36\) or \(\displaystyle 4 x \geq 40\). Isolating \(\displaystyle x\) gives \(\displaystyle x \leq -9\) or \(\displaystyle x \geq 10\).
\begin{question}Solve $| 4 x - 2 | \geq 38$
\soln{9cm}{The inequality is an "or" type compound inequality. This gives the two inequalities $4 x - 2 \leq -38$ or $4 x - 2 \geq 38$. Solving gives $4 x \leq -36$ or $4 x \geq 40$. Isolating $x$ gives $x \leq -9$ or $x \geq 10$. }
\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 | 4 x - 2 | \geq 38 " src="/equation_images/%20%5Cdisplaystyle%20%7C%204%20x%20-%202%20%7C%20%5Cgeq%2038%20" alt="LaTeX: \displaystyle | 4 x - 2 | \geq 38 " data-equation-content=" \displaystyle | 4 x - 2 | \geq 38 " /> </p> </p>
<p> <p>The inequality is an "or" type compound inequality. This gives the two inequalities <img class="equation_image" title=" \displaystyle 4 x - 2 \leq -38 " src="/equation_images/%20%5Cdisplaystyle%204%20x%20-%202%20%5Cleq%20-38%20" alt="LaTeX: \displaystyle 4 x - 2 \leq -38 " data-equation-content=" \displaystyle 4 x - 2 \leq -38 " /> or <img class="equation_image" title=" \displaystyle 4 x - 2 \geq 38 " src="/equation_images/%20%5Cdisplaystyle%204%20x%20-%202%20%5Cgeq%2038%20" alt="LaTeX: \displaystyle 4 x - 2 \geq 38 " data-equation-content=" \displaystyle 4 x - 2 \geq 38 " /> . Solving gives <img class="equation_image" title=" \displaystyle 4 x \leq -36 " src="/equation_images/%20%5Cdisplaystyle%204%20x%20%5Cleq%20-36%20" alt="LaTeX: \displaystyle 4 x \leq -36 " data-equation-content=" \displaystyle 4 x \leq -36 " /> or <img class="equation_image" title=" \displaystyle 4 x \geq 40 " src="/equation_images/%20%5Cdisplaystyle%204%20x%20%5Cgeq%2040%20" alt="LaTeX: \displaystyle 4 x \geq 40 " data-equation-content=" \displaystyle 4 x \geq 40 " /> . 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 -9 " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cleq%20-9%20" alt="LaTeX: \displaystyle x \leq -9 " data-equation-content=" \displaystyle x \leq -9 " /> or <img class="equation_image" title=" \displaystyle x \geq 10 " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cgeq%2010%20" alt="LaTeX: \displaystyle x \geq 10 " data-equation-content=" \displaystyle x \geq 10 " /> . </p> </p>