Final answer:
To solve the inequality 4x+20|+6<10, subtract 6 from both sides, consider the definition of absolute value, and solve the resulting inequalities. This yields the solution interval -6, -4, which can be shown as a shaded region on a number line.
Step-by-step explanation:
The subject of the question involves solving an inequality involving absolute values. This type of problem requires understanding how to manipulate inequalities and absolute value expressions. To solve the inequality |4x+20|+6<10, we first isolate the absolute value expression by subtracting 6 from both sides, which gives us 4x+20 < 4.
Next, we recognize that if the absolute value of something is less than 4, the inside of the absolute value must be between -4 and 4. So we set up two separate inequalities: 4x+20 < 4 and 4x+20 > -4. Solving the first gives x < -4, and solving the second gives x > -6.
Hence, the solution to the inequality is that x is in the interval -6, -4, which can be represented as a shaded area on a number line between these two points.