1) When solving for |x| in the equation 3|x| - 2 = 2|x| + 3, we can simplify by isolating the absolute value term:
3|x| - 2 = 2|x| + |3x| - 2 = |2x| + 3
Since we have two absolute value terms being subtracted, we can rewrite the equation as:
|3x| - |2x| = 3 + 2
This simplifies to|x| = 5
Therefore, the solution for |x| is x = 5 or x = -5.
2) Similarly, we can solve for |x| in the equation 4|x| - 7 = -2|x| + 5:
4|x| - 7 = -2|x| + |4x| - 7 = |-2x| + 5
Similar to the first equation, we have two absolute value terms, and we can rewrite the equation as:
|4x| + 2x = 7 + 5
This simplifies to|x| = 6
Therefore, the solution for |x| is x = 6 or x = -6.
1) When solving for |x| in the equation 3|x| - 2 = 2|x| + 3, we can simplify by isolating the absolute value term:
3|x| - 2 = 2|x| +
|3x| - 2 = |2x| + 3
Since we have two absolute value terms being subtracted, we can rewrite the equation as:
|3x| - |2x| = 3 + 2
This simplifies to
|x| = 5
Therefore, the solution for |x| is x = 5 or x = -5.
2) Similarly, we can solve for |x| in the equation 4|x| - 7 = -2|x| + 5:
4|x| - 7 = -2|x| +
|4x| - 7 = |-2x| + 5
Similar to the first equation, we have two absolute value terms, and we can rewrite the equation as:
|4x| + 2x = 7 + 5
This simplifies to
|x| = 6
Therefore, the solution for |x| is x = 6 or x = -6.