A double inequality example is -c < ax + b < c. This form is best described as

A double inequality example is -c < ax + b < c. This form is best described as

• A. -c < ax + b < c
• B. ax + b < -c or ax + b > c
• C. ax + b > -c and ax + b < c
• D. ax + b ≤ c and ax + b ≥ -c

Answer: (A)

The question tests understanding of a chain (double) inequality, which describes a value lying between two bounds in a single, concise statement. -c < ax + b < c means ax + b is strictly greater than -c and strictly less than c at the same time. The two strict inequalities together enforce that ax + b sits inside the interval (-c, c), with the endpoints excluded. Why this form is best: expressing the idea as a single chained statement clearly communicates the “between” relationship in one compact expression. It shows the simultaneous requirement of both bounds without breaking the idea into separate pieces. If you rewrite it as two separate inequalities joined by "and" (ax + b > -c and ax + b < c), you describe the same set of values, but the chain form is the standard, most direct way to express a value between two numbers. Note: using or would describe values outside the interval, and using non-strict signs (≤ or ≥) would include the endpoints, which isn’t the same as the given strict between.

The question tests understanding of a chain (double) inequality, which describes a value lying between two bounds in a single, concise statement. -c < ax + b < c means ax + b is strictly greater than -c and strictly less than c at the same time. The two strict inequalities together enforce that ax + b sits inside the interval (-c, c), with the endpoints excluded.

Why this form is best: expressing the idea as a single chained statement clearly communicates the “between” relationship in one compact expression. It shows the simultaneous requirement of both bounds without breaking the idea into separate pieces. If you rewrite it as two separate inequalities joined by "and" (ax + b > -c and ax + b < c), you describe the same set of values, but the chain form is the standard, most direct way to express a value between two numbers.

Note: using or would describe values outside the interval, and using non-strict signs (≤ or ≥) would include the endpoints, which isn’t the same as the given strict between.