Question

5|x| + 3 = 71,7|x|+4,9=102,5|3y|=15​

Answer 1

1.X=7-3

X=4

2.4,9=10

3.2,5•3x[y]=15

7,5x[y]=15

y=2

y=-2

y=-2,y•=2

1 2

Answer 2

To solve the equations involving absolute values, we need to consider both the positive and negative values of the expressions inside the absolute value bars. Let's solve each equation step by step:

1. 5|x| + 3 = 71:

First, we isolate the absolute value expression by subtracting 3 from both sides:

5|x| = 71 - 3 5|x| = 68

Next, divide both sides by 5:

|x| = 68/5 |x| = 13.6

Now, we have two cases to consider for |x|:

Case 1: x = 13.6 Case 2: x = -13.6

2. 7|x| + 4.9 = 102.5:

Similar to the previous equation, we isolate the absolute value expression:

7|x| = 102.5 - 4.9 7|x| = 97.6

Divide both sides by 7:

|x| = 97.6/7 |x| = 13.942857142857143

Again, consider both cases for |x|:

Case 1: x = 13.942857142857143 Case 2: x = -13.942857142857143

3. |3y| = 15:

We don't have an additional constant term, so we directly solve for |3y|:

|3y| = 15

Now, consider both cases for |3y|:

Case 1: 3y = 15 Case 2: 3y = -15

Now, we solve for y for each case:

Case 1: 3y = 15 Divide both sides by 3: y = 15/3 y = 5

Case 2: 3y = -15 Divide both sides by 3: y = -15/3 y = -5

So, the solutions to the given equations are: x = 13.6 or x = -13.6 x = 13.942857142857143 or x = -13.942857142857143 y = 5 or y = -5