Question

Solve the literal equation |ax + b1| = c for x.

a) x = (c - b1) / a
b) x = (-c - b1) / a
c) x = (b1 - c) / a
d) x = (-b1 - c) / a

Answer 1

The equation |ax + b1| = c has two possible solutions for x: x = (c - b1) / a and x = (-c - b1) / a, due to the properties of the absolute value function.

Step-by-step explanation:

To solve the literal equation |ax + b1| = c for x, we need to consider the definition of the absolute value. The absolute value of a number is positive if the number is positive, and it is the negative of the number if the number is negative. Therefore, we have two cases:

• If ax + b1 is positive, then ax + b1 = c. Solving this for x gives x = (c - b1) / a.
• If ax + b1 is negative, then ax + b1 = -c. In this case, solving for x gives x = (-c - b1) / a.

Therefore, the complete solution for x is given by both x = (c - b1) / a and x = (-c - b1) / a.