How many solutions does the equation have? 7=vert zvert +4 no solution one solution two solutions

## Step 1<br />The given equation is \(7 = |z| + 4\). The absolute value of a number, denoted as \(|z|\), is always non-negative. This means that the absolute value of any number, whether it's positive, negative, or zero, is always a non-negative number.<br /><br />## Step 2<br />The equation can be rearranged to \(|z| = 7 - 4\), which simplifies to \(|z| = 3\).<br /><br />## Step 3<br />The absolute value equation \(|z| = 3\) has two solutions. This is because the absolute value of a number is the distance of that number from zero on the number line. Therefore, if \(|z| = 3\), then \(z\) can be either 3 units to the right of zero (which is 3) or 3 units to the left of zero (which is -3).