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Solve \(\displaystyle | x - 1 | \geq 13\)

The inequality is an "or" type compound inequality. This gives the two inequalities \(\displaystyle x - 1 \leq -13\) or \(\displaystyle x - 1 \geq 13\). Solving gives \(\displaystyle x \leq -12\) or \(\displaystyle x \geq 14\). Isolating \(\displaystyle x\) gives \(\displaystyle x \leq -12\) or \(\displaystyle x \geq 14\).

Download \(\LaTeX\) 

\begin{question}Solve $| x - 1 | \geq 13$
    \soln{9cm}{The inequality is an "or" type compound inequality. This gives the two inequalities $x - 1 \leq -13$ or $x - 1 \geq 13$. Solving gives $x \leq -12$ or $x \geq 14$. Isolating $x$ gives $x \leq -12$ or $x \geq 14$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>Solve  <img class="equation_image" title=" \displaystyle | x - 1 | \geq 13 " src="/equation_images/%20%5Cdisplaystyle%20%7C%20x%20-%201%20%7C%20%5Cgeq%2013%20" alt="LaTeX:  \displaystyle | x - 1 | \geq 13 " data-equation-content=" \displaystyle | x - 1 | \geq 13 " /> </p> </p>
HTML for Canvas
<p> <p>The inequality is an "or" type compound inequality. This gives the two inequalities  <img class="equation_image" title=" \displaystyle x - 1 \leq -13 " src="/equation_images/%20%5Cdisplaystyle%20x%20-%201%20%5Cleq%20-13%20" alt="LaTeX:  \displaystyle x - 1 \leq -13 " data-equation-content=" \displaystyle x - 1 \leq -13 " />  or  <img class="equation_image" title=" \displaystyle x - 1 \geq 13 " src="/equation_images/%20%5Cdisplaystyle%20x%20-%201%20%5Cgeq%2013%20" alt="LaTeX:  \displaystyle x - 1 \geq 13 " data-equation-content=" \displaystyle x - 1 \geq 13 " /> . Solving gives  <img class="equation_image" title=" \displaystyle x \leq -12 " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cleq%20-12%20" alt="LaTeX:  \displaystyle x \leq -12 " data-equation-content=" \displaystyle x \leq -12 " />  or  <img class="equation_image" title=" \displaystyle x \geq 14 " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cgeq%2014%20" alt="LaTeX:  \displaystyle x \geq 14 " data-equation-content=" \displaystyle x \geq 14 " /> . 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 -12 " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cleq%20-12%20" alt="LaTeX:  \displaystyle x \leq -12 " data-equation-content=" \displaystyle x \leq -12 " />  or  <img class="equation_image" title=" \displaystyle x \geq 14 " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cgeq%2014%20" alt="LaTeX:  \displaystyle x \geq 14 " data-equation-content=" \displaystyle x \geq 14 " /> . </p> </p>