Divide each term by <span>66</span> and simplify. <span><span><span>|6−4x|</span>=<span><span>4x</span>3</span>+<span>23</span></span><span><span>|6-4x|</span>=<span><span>4x</span>3</span>+<span>23</span></span></span>Remove the absolute value term. This creates a <span>±±</span> on the right side of the equation because <span><span><span>|x|</span>=±x</span><span><span>|x|</span>=±x</span></span>.<span><span>6−4x=±<span><span>4x</span>3</span>+<span>23</span></span><span>6-4x=±<span><span>4x</span>3</span>+<span>23</span></span></span>Set up the positive portion of the <span>±±</span> solution.<span><span>6−4x=<span><span>4x</span>3</span>+<span>23</span></span><span>6-4x=<span><span>4x</span>3</span>+<span>23</span></span></span>Solve the first equation for <span>xx</span>..<span><span>x=1</span><span>x=1</span></span>Set up the negative portion of the <span>±±</span> solution.<span><span>6−4x=−<span>(<span><span>4x</span>3</span>+<span>23</span>)</span></span><span>6-4x=-<span>(<span><span>4x</span>3</span>+<span>23</span>)</span></span></span>Move <span>xx</span> to the right side of the equation by subtracting <span>xx</span> from both sides of the equation.<span><span>−<span><span>8x</span>3</span>=−<span>203</span></span><span>-<span><span>8x</span>3</span>=-<span>203</span></span></span>Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.<span><span><span>(−8x)</span>⋅<span>(3)</span>=<span>(3)</span>⋅<span>(−20)</span></span><span><span>(-8x)</span>⋅<span>(3)</span>=<span>(3)</span>⋅<span>(-20)</span></span></span>Solve the equation for <span>xx</span>..<span><span>x=<span>52</span></span><span>x=<span>52</span></span></span>The solution to the equation includes both the positive and negative portions of the solution.<span>x=1,<span><span>52</span></span></span>
