Step 1: Simplify both sides of the equation.<span><span><span>3x</span>+<span>2<span>(<span>x−9</span>)</span></span></span>=<span><span><span>8x</span>+x</span>−14</span></span><span><span><span><span>3x</span>+<span><span>(2)</span><span>(x)</span></span></span>+<span><span>(2)</span><span>(<span>−9</span>)</span></span></span>=<span><span><span><span>8x</span>+x</span>+</span>−14</span></span>(Distribute)<span><span><span><span><span>3x</span>+<span>2x</span></span>+</span>−18</span>=<span><span><span><span>8x</span>+x</span>+</span>−14</span></span><span><span><span>(<span><span>3x</span>+<span>2x</span></span>)</span>+<span>(<span>−18</span>)</span></span>=<span><span>(<span><span>8x</span>+x</span>)</span>+<span>(<span>−14</span>)</span></span></span>(Combine Like Terms)<span><span><span>5x</span>+<span>−18</span></span>=<span><span>9x</span>+<span>−14</span></span></span><span><span><span>5x</span>−18</span>=<span><span>9x</span>−14</span></span>Step 2: Subtract 9x from both sides.<span><span><span><span>5x</span>−18</span>−<span>9x</span></span>=<span><span><span>9x</span>−14</span>−<span>9x</span></span></span><span><span><span>−<span>4x</span></span>−18</span>=<span>−14</span></span>Step 3: Add 18 to both sides.<span><span><span><span>−<span>4x</span></span>−18</span>+18</span>=<span><span>−14</span>+18</span></span><span><span>−<span>4x</span></span>=4</span>Step 4: Divide both sides by -4.<span><span><span>−<span>4x</span></span><span>−4</span></span>=<span>4<span>−4</span></span></span><span>x=<span>−1</span></span>
The parallelogram forms two right triangles and since it's a parallelogram the opposite angles are congruent meaning you can say the triangles are similar through AA~. The ratio is 2:3 and FA =12 making AE= 8
