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Solve \(\displaystyle | 4 x - 2 | \geq 26\)
The inequality is an "or" type compound inequality. This gives the two inequalities \(\displaystyle 4 x - 2 \leq -26\) or \(\displaystyle 4 x - 2 \geq 26\). Solving gives \(\displaystyle 4 x \leq -24\) or \(\displaystyle 4 x \geq 28\). Isolating \(\displaystyle x\) gives \(\displaystyle x \leq -6\) or \(\displaystyle x \geq 7\).
\begin{question}Solve $| 4 x - 2 | \geq 26$
\soln{9cm}{The inequality is an "or" type compound inequality. This gives the two inequalities $4 x - 2 \leq -26$ or $4 x - 2 \geq 26$. Solving gives $4 x \leq -24$ or $4 x \geq 28$. Isolating $x$ gives $x \leq -6$ or $x \geq 7$. }
\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 26 " src="/equation_images/%20%5Cdisplaystyle%20%7C%204%20x%20-%202%20%7C%20%5Cgeq%2026%20" alt="LaTeX: \displaystyle | 4 x - 2 | \geq 26 " data-equation-content=" \displaystyle | 4 x - 2 | \geq 26 " /> </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 -26 " src="/equation_images/%20%5Cdisplaystyle%204%20x%20-%202%20%5Cleq%20-26%20" alt="LaTeX: \displaystyle 4 x - 2 \leq -26 " data-equation-content=" \displaystyle 4 x - 2 \leq -26 " /> or <img class="equation_image" title=" \displaystyle 4 x - 2 \geq 26 " src="/equation_images/%20%5Cdisplaystyle%204%20x%20-%202%20%5Cgeq%2026%20" alt="LaTeX: \displaystyle 4 x - 2 \geq 26 " data-equation-content=" \displaystyle 4 x - 2 \geq 26 " /> . Solving gives <img class="equation_image" title=" \displaystyle 4 x \leq -24 " src="/equation_images/%20%5Cdisplaystyle%204%20x%20%5Cleq%20-24%20" alt="LaTeX: \displaystyle 4 x \leq -24 " data-equation-content=" \displaystyle 4 x \leq -24 " /> or <img class="equation_image" title=" \displaystyle 4 x \geq 28 " src="/equation_images/%20%5Cdisplaystyle%204%20x%20%5Cgeq%2028%20" alt="LaTeX: \displaystyle 4 x \geq 28 " data-equation-content=" \displaystyle 4 x \geq 28 " /> . 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 -6 " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cleq%20-6%20" alt="LaTeX: \displaystyle x \leq -6 " data-equation-content=" \displaystyle x \leq -6 " /> or <img class="equation_image" title=" \displaystyle x \geq 7 " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cgeq%207%20" alt="LaTeX: \displaystyle x \geq 7 " data-equation-content=" \displaystyle x \geq 7 " /> . </p> </p>