11. 2<span><span><span>+6x</span>+4</span>=<span>3x+12</span></span>Step 1: Simplify both sides of the equation.<span><span><span>2+6x</span>+4</span>=<span>3x+12</span></span><span><span><span>(6x)</span>+<span>(2+4)</span></span>=<span>3x+12</span></span>(Combine Like Terms)<span><span>6x+6</span>=<span>3x+12</span></span><span><span>6x+6</span>=<span>3x+12</span></span>Step 2: Subtract 3x from both sides.<span><span><span>6x+6</span>−3x</span>=<span><span>3x+12</span>−3x</span></span><span><span>3x+6</span>=12</span>Step 3: Subtract 6 from both sides.<span><span><span>3x+6</span>−6</span>=12−6</span><span>3x=6</span>Step 4: Divide both sides by 3.<span><span>3x3</span>=63</span>x=2Answer:x=212.−<span><span><span>5+<span>8x</span></span>+2</span>=<span><span>4x</span>+4</span></span>Step 1: Simplify both sides of the equation.<span><span><span><span>−5</span>+<span>8x</span></span>+2</span>=<span><span>4x</span>+4</span></span><span><span><span>(<span>8x</span>)</span>+<span>(<span><span>−5</span>+2</span>)</span></span>=<span><span>4x</span>+4</span></span>(Combine Like Terms)<span><span><span>8x</span>+<span>−3</span></span>=<span><span>4x</span>+4</span></span><span><span><span>8x</span>−3</span>=<span><span>4x</span>+4</span></span>Step 2: Subtract 4x from both sides.<span><span><span><span>8x</span>−3</span>−<span>4x</span></span>=<span><span><span>4x</span>+4</span>−<span>4x</span></span></span><span><span><span>4x</span>−3</span>=4</span>Step 3: Add 3 to both sides.<span><span><span><span>4x</span>−3</span>+3</span>=<span>4+3</span></span><span><span>4x</span>=7</span>Step 4: Divide both sides by 4.<span><span><span>4x</span>4</span>=<span>7/4</span></span><span>x=<span>7/4</span></span>Answer:<span>x=<span>7/4</span></span>
This information will be modeled using the formula thus we shall have: Sn=ar^n where: a=first term r=common ratio from the information: a=30 ft r=60/100=3/5=0.6 therefore the formula will be Sn=30(0.6)^n where n is the number of terms: thus when n=5 th sum will be: S5=30(0.6)^5 S5=30(0.6)^5 S5=2.33 ft Answer: 2.33 ft
