Video Transcript
What is the solution set of the equation six multiplied by the modulus of 𝑥 is equal to negative seven multiplied by the modulus of 𝑥 plus 20?
We will begin to solve this question by trying to isolate the modulus of 𝑥 on one side of our equation. We do this by adding seven multiplied by the modulus of 𝑥 to both sides. Collecting like terms on the left-hand side gives us 13 multiplied by the modulus or absolute value of 𝑥. This is equal to 20. Dividing both sides of this equation by 13, the modulus or absolute value of 𝑥 is equal to 20 over 13.
We know that the modulus of a number gives us the distance of this number from zero. Both positive and negative 20 over 13 are a distance of 20 over 13 away from zero. This means that 𝑥 could be equal to either of these values. Written using set notation, we have two solutions: negative 20 over 13 and 20 over 13.
