Write the solution of the absolute value inequality the absolute value of (x - 7) less than or equal to 3.

1. An absolute value at most 3 means the distance from the inside expression to zero is at most 3. 2. So the inside expression lies between negative 3 and 3 inclusive. 3. Write that as negative 3 less than or equal to x minus 7, which is less than or equal to 3. 4. Add 7 to all three parts to isolate x. 5. The left end becomes negative 3 plus 7, which is 4. 6. The right end becomes 3 plus 7, which is 10. 7. Both signs allow equality, so both endpoints are included and take brackets. 8. The solution is therefore the closed interval from 4 to 10. 9. The interval [3, 11] adds and subtracts around the wrong centre. 10. The interval [7, 10] keeps only the half of the solution above the centre. _Source: OpenStax College Algebra (CC BY 4.0), section 2.7 Linear Inequalities and Absolute Value Inequalities_