Question

For y=3|7-2×|+5 which set describes x when y<8

Answer 1

To find the set that describes x when y<8 for the equation y=3|7-2×|+5, we need to solve the inequality y<8 and find the range of x values. The set that describes x when y<8 is {3,4}.

Step-by-step explanation:

In order to find the set that describes x when y<8 for the equation y=3|7-2×|+5, we need to solve the inequality y<8 to find the range of x values. Let's break down the steps:

1. Substitute y with 8: 8=3|7-2×|+5
2. Subtract 5 from both sides: 3|7-2×| = 3
3. Divide both sides by 3: |7-2×| = 1
4. Split the equation into two cases: 7-2×=1 and -(7-2×)=1
5. Solve each case separately: 7-2×=1 -> -2×=-6 -> x=3 and -(7-2×)=1 -> -7+2×=1 -> 2×=8 -> x=4
6. Combine the solutions: x=3,4

Therefore, the set that describes x when y<8 for the given equation is {3,4}.