Let's solve your equation step-by-step.<span><span>−<span>7<span>(<span>k+9</span>)</span></span></span>=<span><span>9<span>(<span>k−5</span>)</span></span>−<span>14k</span></span></span>Step 1: Simplify both sides of the equation.<span><span>−<span>7<span>(<span>k+9</span>)</span></span></span>=<span><span>9<span>(<span>k−5</span>)</span></span>−<span>14k</span></span></span><span><span><span><span>(<span>−7</span>)</span><span>(k)</span></span>+<span><span>(<span>−7</span>)</span><span>(9)</span></span></span>=<span><span><span><span><span>(9)</span><span>(k)</span></span>+<span><span>(9)</span><span>(<span>−5</span>)</span></span></span>+</span>−<span>14k</span></span></span>(Distribute)<span><span><span><span>−<span>7k</span></span>+</span>−63</span>=<span><span><span><span><span>9k</span>+</span>−45</span>+</span>−<span>14k</span></span></span><span><span><span>−<span>7k</span></span>−63</span>=<span><span>(<span><span>9k</span>+<span>−<span>14k</span></span></span>)</span>+<span>(<span>−45</span>)</span></span></span>(Combine Like Terms)<span><span><span>−<span>7k</span></span>−63</span>=<span><span>−<span>5k</span></span>+<span>−45</span></span></span><span><span><span>−<span>7k</span></span>−63</span>=<span><span>−<span>5k</span></span>−45</span></span>Step 2: Add 5k to both sides.<span><span><span><span>−<span>7k</span></span>−63</span>+<span>5k</span></span>=<span><span><span>−<span>5k</span></span>−45</span>+<span>5k</span></span></span><span><span><span>−<span>2k</span></span>−63</span>=<span>−45</span></span>Step 3: Add 63 to both sides.<span><span><span><span>−<span>2k</span></span>−63</span>+63</span>=<span><span>−45</span>+63</span></span><span><span>−<span>2k</span></span>=18</span>Step 4: Divide both sides by -2.<span><span><span>−<span>2k</span></span><span>−2</span></span>=<span>18<span>−2</span></span></span><span>k=<span>−9</span></span>Answer:<span>k=<span>−9</span></span>
