Question

|3+x|=2 |6-X|=4 |2x+2|=8 |8-2x|=10 |6+3x|=9 3|x+4|-7=18 геометрии и аналитически

Answer 1

1. 3+x=2
3+x=-2
x=2-3
x=-2-3
x=-1
x=-5

Answer 2

Solving the Equations

To solve the given set of equations, we'll start by solving each equation individually.

1. Equation 1: |3x-9|=6 - The solution for this equation is: x=5, x=1.

2. Equation 2: |2x-8|-|x+1|=-2 - The solution for this equation is: x=-4, x=2.

3. Equation 3: |2x+2|=8 - The solution for this equation is: x=3, x=-5.

4. Equation 4: |8-2x|=10 - The solution for this equation is: x=-1, x=9.

5. Equation 5: |6+3x|=9 - The solution for this equation is: x=1, x=-5.

6. Equation 6: 3|x+4|-7=18 - The solution for this equation is: x=-9, x=8.

Geometric and Analytical Interpretation

The solutions to the given equations can be interpreted geometrically and analytically. Geometrically, the absolute value equations represent the distance between a point and the origin on a number line. Analytically, the solutions represent the values of x that satisfy the given equations.

By solving the equations and understanding their geometric and analytical interpretations, we have found the solutions for each equation and provided a brief explanation of their geometric and analytical significance.