Let's solve your equation step-by-step.<span><span>−<span>4<span>(<span>r+2</span>)</span></span></span>=<span>4<span>(<span>2−<span>4r</span></span>)</span></span></span>Step 1: Simplify both sides of the equation.<span><span>−<span>4<span>(<span>r+2</span>)</span></span></span>=<span>4<span>(<span>2−<span>4r</span></span>)</span></span></span><span>Simplify</span><span><span><span><span>(<span>−4</span>)</span><span>(r)</span></span>+<span><span>(<span>−4</span>)</span><span>(2)</span></span></span>=<span><span><span>(4)</span><span>(2)</span></span>+<span><span>(4)</span><span>(<span>−<span>4r</span></span>)</span></span></span></span>(Distribute)<span><span><span><span>−<span>4r</span></span>+</span>−8</span>=<span><span>8+</span>−<span>16r</span></span></span><span><span><span>−<span>4r</span></span>−8</span>=<span><span>−<span>16r</span></span>+8</span></span>Step 2: Add 16r to both sides.<span><span><span><span>−<span>4r</span></span>−8</span>+<span>16r</span></span>=<span><span><span>−<span>16r</span></span>+8</span>+<span>16r</span></span></span><span><span><span>12r</span>−8</span>=8</span>Step 3: Add 8 to both sides.<span><span><span><span>12r</span>−8</span>+8</span>=<span>8+8</span></span><span><span>12r</span>=16</span>Step 4: Divide both sides by 12.<span><span><span>12r</span>12</span>=<span>1612</span></span><span>r=<span>43</span></span>Answer:<span>r=<span>4<span>3</span></span></span>
The answer is translation of 2 units left and a reflection over the x-axis.
The triangle is translated 2 units left because the triangle moved two units to the left and it is reflected over the x-axis because the bottom triangle is like a reflection of the original triangle.
