21. Simplifying 6 + -2(x + 6) = 3x + 4 Reorder the terms: 6 + -2(6 + x) = 3x + 4 6 + (6 * -2 + x * -2) = 3x + 4 6 + (-12 + -2x) = 3x + 4 Combine like terms: 6 + -12 = -6 -6 + -2x = 3x + 4 Reorder the terms: -6 + -2x = 4 + 3x Solving -6 + -2x = 4 + 3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3x' to each side of the equation. -6 + -2x + -3x = 4 + 3x + -3x Combine like terms: -2x + -3x = -5x -6 + -5x = 4 + 3x + -3x Combine like terms: 3x + -3x = 0 -6 + -5x = 4 + 0 -6 + -5x = 4 Add '6' to each side of the equation. -6 + 6 + -5x = 4 + 6 Combine like terms: -6 + 6 = 0 0 + -5x = 4 + 6 -5x = 4 + 6 Combine like terms: 4 + 6 = 10 -5x = 10 Divide each side by '-5'. x = -2 Simplifying x = -2
22.Reorder the terms: 3x + 2(-1 + x) = 9x + 4 3x + (-1 * 2 + x * 2) = 9x + 4 3x + (-2 + 2x) = 9x + 4 Reorder the terms: -2 + 3x + 2x = 9x + 4 Combine like terms: 3x + 2x = 5x -2 + 5x = 9x + 4 Reorder the terms: -2 + 5x = 4 + 9x Solving -2 + 5x = 4 + 9x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9x' to each side of the equation. -2 + 5x + -9x = 4 + 9x + -9x Combine like terms: 5x + -9x = -4x -2 + -4x = 4 + 9x + -9x Combine like terms: 9x + -9x = 0 -2 + -4x = 4 + 0 -2 + -4x = 4 Add '2' to each side of the equation. -2 + 2 + -4x = 4 + 2 Combine like terms: -2 + 2 = 0 0 + -4x = 4 + 2 -4x = 4 + 2 Combine like terms: 4 + 2 = 6 -4x = 6 Divide each side by '-4'. x = -1.5 Simplifying x = -1.5
23.Reorder the terms: 5(-2 + x) + x = 6(x + 3) + -4x (-2 * 5 + x * 5) + x = 6(x + 3) + -4x (-10 + 5x) + x = 6(x + 3) + -4x Combine like terms: 5x + x = 6x -10 + 6x = 6(x + 3) + -4x Reorder the terms: -10 + 6x = 6(3 + x) + -4x -10 + 6x = (3 * 6 + x * 6) + -4x -10 + 6x = (18 + 6x) + -4x Combine like terms: 6x + -4x = 2x -10 + 6x = 18 + 2x Solving -10 + 6x = 18 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -10 + 6x + -2x = 18 + 2x + -2x Combine like terms: 6x + -2x = 4x -10 + 4x = 18 + 2x + -2x Combine like terms: 2x + -2x = 0 -10 + 4x = 18 + 0 -10 + 4x = 18 Add '10' to each side of the equation. -10 + 10 + 4x = 18 + 10 Combine like terms: -10 + 10 = 0 0 + 4x = 18 + 10 4x = 18 + 10 Combine like terms: 18 + 10 = 28 4x = 28 Divide each side by '4'. x = 7 Simplifying x = 7
24.Combine like terms: 2 + -12 = -10 -10 + 3x = 5(2 + -1x) + 4x -10 + 3x = (2 * 5 + -1x * 5) + 4x -10 + 3x = (10 + -5x) + 4x Combine like terms: -5x + 4x = -1x -10 + 3x = 10 + -1x Solving -10 + 3x = 10 + -1x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'x' to each side of the equation. -10 + 3x + x = 10 + -1x + x Combine like terms: 3x + x = 4x -10 + 4x = 10 + -1x + x Combine like terms: -1x + x = 0 -10 + 4x = 10 + 0 -10 + 4x = 10 Add '10' to each side of the equation. -10 + 10 + 4x = 10 + 10 Combine like terms: -10 + 10 = 0 0 + 4x = 10 + 10 4x = 10 + 10 Combine like terms: 10 + 10 = 20 4x = 20 Divide each side by '4'. x = 5 Simplifying x = 5
