Algebra

4z + 3 = 6 + 2z leads to 2z = 3, so z = 1.5 or 3/2. Given z = 3/m, we have 3/2 = 3/m, which implies m = 2.

2y + 5/3 = 26/3 - y. Adding y to both sides and subtracting 5/3 gives 3y = 21/3 = 7. So y = 7/3. Given y = 7/m, m must be 3.

sqrt(5-x) = x * sqrt(5-x). This implies sqrt(5-x) * (1 - x) = 0. Thus, 5-x = 0 (x=5) or 1-x = 0 (x=1). Both are valid roots.

Let u = sqrt(x). The equation becomes 3u^2 - 7u + 2 = 0. Factoring gives (3u - 1)(u - 2) = 0. So u = 1/3 or u = 2. Squaring gives x = 1/9 or x = 4.

Test roots: If x=2, 2^3 + 2^2 + 12 = 8 + 4 + 12 = 24. Correct. If x=1, 1^3 + 1^2 + 12 = 1 + 1 + 12 = 14, not 24. So the statement is false.

Substituting x = -3 into 2x^2 + 2x + 2 gives 2(9) - 6 + 2 = 14, not 0. Substituting x = 1 gives 2 + 2 + 2 = 6, not 0. Therefore, the statement is false.

The equation (3/5)x = 15 simplifies to x = 15 * (5/3) = 25. Checking the options: 5x = 125 gives x = 25.

2a - 2 = 4 - 4a => 6a = 6 => a = 1. The only root is 1, not -1. Thus, the statement is false.

-5x + 3 = x + 2. Subtract x from both sides: -6x + 3 = 2. Subtract 3 from both sides: -6x = -1. Divide by -6: x = 1/6.

6 + 4x = 6x - 10. Subtract 4x from both sides: 6 = 2x - 10. Add 10 to both sides: 16 = 2x. Divide by 2: x = 8.

x + 3(2x + 5) = -20 => x + 6x + 15 = -20 => 7x = -35 => x = -5.

3(2x+5) = 6x + 15. 10x + 7 + 2(x-8) = 10x + 7 + 2x - 16 = 12x - 9. Set 6x + 15 = 12x - 9. 24 = 6x, so x = 4.

6 + 64 - 16x = 14 - 32x + 16. 70 - 16x = 30 - 32x. 16x = -40. x = -40/16 = -5/2.

(2x+3)/5 - 10 = (4-3x)/2. Multiply by 10: 2(2x+3) - 100 = 5(4-3x) => 4x + 6 - 100 = 20 - 15x => 19x = 114 => x = 6.