2(|x−3|)−4≥10 Step 1: Add 4 to both sides.<span><span><span><span>2<span>(<span>|<span>x−3</span>|</span>)</span></span>−4</span>+4</span>≥<span>10+4</span></span><span><span>2<span>(<span>|<span>x−3</span>|</span>)</span></span>≥14</span>Step 2: Divide both sides by 2.<span><span><span>2<span>(<span>|<span>x−3</span>|</span>)</span></span>2</span>≥<span>142</span></span><span><span>|<span>x−3</span>|</span>≥7</span>Step 3: Solve Absolute Value.<span><span>|<span>x−3</span>|</span>≥7</span>We know either<span><span>x−3</span>≥7</span>or<span><span>x−3</span>≤<span>−7</span></span><span><span>x−3</span>≥7</span>(Possibility 1)<span><span><span>x−3</span>+3</span>≥<span>7+3</span></span>(Add 3 to both sides)<span>x≥10</span><span><span>x−3</span>≤<span>−7</span></span>(Possibility 2)<span><span><span>x−3</span>+3</span>≤<span><span>−7</span>+3</span></span>(Add 3 to both sides)<span>x≤<span>−<span>4 the answer is </span></span></span><span>x≥<span><span>10<span>or </span></span>x</span></span>≤−4
Lets first solve the first equation which is x - 3 ≥ 7 and that would be x ≥ 10 and lets solve the other one which is -(x - 3) ≥ 7 and that would be x <span>≤</span> -4
