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 1The 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.## Step 2The 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 . The absolute value inequality is given by .## Step 3The 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.## Step 4Substituting the mean value and tolerance into the absolute value inequality, we get .## Step 5The 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 . The compound inequality is given by .## Step 6Substituting the mean value and tolerance into the compound inequality, we get .