Question

Solve the following equations: Justify the steps used to solve a linear equation 1. | 3x | = 6 2. 2 | x-7 | = 12 3. | 3x - 4 | + 5 = 32 4. 5 | 2x-3 | = 15 5. 1/2 |4x -8 | - 4 = 3 ​

Answer 1

To solve linear equations with absolute values, isolate the variable within the absolute value signs by following specific steps.

Step-by-step explanation:

To solve the given linear equations, we need to isolate the variable within the absolute value signs. Here are the steps to solve each equation:

1. Solve |3x| = 6 by considering the positive and negative solutions for 3x.
2. Solve 2|x-7| = 12 by separating the equation into two cases.
3. Solve |3x - 4| + 5 = 32 by subtracting 5 from both sides and then isolating the absolute value expression.
4. Solve 5|2x-3| = 15 by dividing both sides by 5 and then solving for the absolute value expression.
5. Solve 1/2|4x - 8| - 4 = 3 by adding 4 to both sides, multiplying both sides by 2, and then solving for the absolute value expression.