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Simplifying 0.2k + -1(k + 0.34) = 0.67(k + 3) Reorder the terms: 0.2k + -1(0.34 + k) = 0.67(k + 3) 0.2k + (0.34 * -1 + k * -1) = 0.67(k + 3) 0.2k + (-0.34 + -1k) = 0.67(k + 3) Reorder the terms: -0.34 + 0.2k + -1k = 0.67(k + 3) Combine like terms: 0.2k + -1k = -0.8k -0.34 + -0.8k = 0.67(k + 3) Reorder the terms: -0.34 + -0.8k = 0.67(3 + k) -0.34 + -0.8k = (3 * 0.67 + k * 0.67) -0.34 + -0.8k = (2.01 + 0.67k) Solving -0.34 + -0.8k = 2.01 + 0.67k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.67k' to each side of the equation. -0.34 + -0.8k + -0.67k = 2.01 + 0.67k + -0.67k Combine like terms: -0.8k + -0.67k = -1.47k -0.34 + -1.47k = 2.01 + 0.67k + -0.67k Combine like terms: 0.67k + -0.67k = 0.00 -0.34 + -1.47k = 2.01 + 0.00 -0.34 + -1.47k = 2.01 Add '0.34' to each side of the equation. -0.34 + 0.34 + -1.47k = 2.01 + 0.34 Combine like terms: -0.34 + 0.34 = 0.00 0.00 + -1.47k = 2.01 + 0.34 -1.47k = 2.01 + 0.34 Combine like terms: 2.01 + 0.34 = 2.35 -1.47k = 2.35 Divide each side by '-1.47'. k = -1.598639456 Simplifying k = -1.598639456
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