Write an absolute value inequality and a compound inequality for a length of 9.02 mm with a tolerance of 098 mm. The absolute value inequality is vert x-square vert leqslant square . (Use integers or decimals for any numbers in the inequality.)

## Step 1<br />The problem asks us to write an absolute value inequality and a compound inequality for a length of 9.02 mm with a tolerance of 0.98 mm.<br /><br />## Step 2<br />The absolute value inequality is a mathematical expression that represents the range of values that a variable can take. In this case, the variable is the length of an object, represented by \(x\). The absolute value inequality is given by \(|x - \text{mean value}| \leq \text{tolerance}\).<br /><br />## Step 3<br />The mean value is the average value of the length, which is 9.02 mm. The tolerance is the range within which the length can vary, which is 0.98 mm.<br /><br />## Step 4<br />Substituting the mean value and tolerance into the absolute value inequality, we get \(|x - 9.02| \leq 0.98\).<br /><br />## Step 5<br />The compound inequality is a mathematical expression that represents the range of values that a variable can take. In this case, the variable is the length of an object, represented by \(x\). The compound inequality is given by \(\text{mean value} - \text{tolerance} \leq x \leq \text{mean value} + \text{tolerance}\).<br /><br />## Step 6<br />Substituting the mean value and tolerance into the compound inequality, we get \(9.02 - 0.98 \leq x \leq 9.02 + 0.98\).