1) -3x + 5 = -4-3x = -4 - 5-3x = -9x = 3
2) -4x + 3 = 7-4x = 7 - 3-4x = 4x = -1
3) 8(9 + x) = -472 + 8x = -48x = -76x = -9.5
4) 6x + 10(7 + 5x) = -9x + 56x + 70 + 50x = -9x + 565x + 70 = -9x + 574x = -65x = -0.878
5) 3x + 4(-7 + 6x) = 7x + 63x - 28 + 24x = 7x + 627x - 28 = 7x + 620x = 34x = 1.7
6) (x + 9)² = (10 - x)²x² + 18x + 81 = 100 - 20x + x²18x + 81 = 100 - 20x38x = 19x ≈ 0.5
7) -2x² - 2x + 5 = -x² - x - (1 + x²)-2x² - 2x + 5 = -x² - x - 1 - x²-2x² - 2x + 5 = -2x² - 2x - 15 = -1This equation has no solution
8) (x + 10)² + (x + 6)² = 2x²x² + 20x + 100 + x² + 12x + 36 = 2x²2x² + 32x + 136 = 2x²32x = -136x = -4.25
These are the solutions to the given equations.
1) -3x + 5 = -4
-3x = -4 - 5
-3x = -9
x = 3
2) -4x + 3 = 7
-4x = 7 - 3
-4x = 4
x = -1
3) 8(9 + x) = -4
72 + 8x = -4
8x = -76
x = -9.5
4) 6x + 10(7 + 5x) = -9x + 5
6x + 70 + 50x = -9x + 5
65x + 70 = -9x + 5
74x = -65
x = -0.878
5) 3x + 4(-7 + 6x) = 7x + 6
3x - 28 + 24x = 7x + 6
27x - 28 = 7x + 6
20x = 34
x = 1.7
6) (x + 9)² = (10 - x)²
x² + 18x + 81 = 100 - 20x + x²
18x + 81 = 100 - 20x
38x = 19
x ≈ 0.5
7) -2x² - 2x + 5 = -x² - x - (1 + x²)
-2x² - 2x + 5 = -x² - x - 1 - x²
-2x² - 2x + 5 = -2x² - 2x - 1
5 = -1
This equation has no solution
8) (x + 10)² + (x + 6)² = 2x²
x² + 20x + 100 + x² + 12x + 36 = 2x²
2x² + 32x + 136 = 2x²
32x = -136
x = -4.25
These are the solutions to the given equations.