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Simplifying 5(7 + -5(6 + -1b)) + -7 = 7(5(7b + -6) + 4) + -50 5(7 + (6 * -5 + -1b * -5)) + -7 = 7(5(7b + -6) + 4) + -50 5(7 + (-30 + 5b)) + -7 = 7(5(7b + -6) + 4) + -50 Combine like terms: 7 + -30 = -23 5(-23 + 5b) + -7 = 7(5(7b + -6) + 4) + -50 (-23 * 5 + 5b * 5) + -7 = 7(5(7b + -6) + 4) + -50 (-115 + 25b) + -7 = 7(5(7b + -6) + 4) + -50 Reorder the terms: -115 + -7 + 25b = 7(5(7b + -6) + 4) + -50 Combine like terms: -115 + -7 = -122 -122 + 25b = 7(5(7b + -6) + 4) + -50 Reorder the terms: -122 + 25b = 7(5(-6 + 7b) + 4) + -50 -122 + 25b = 7((-6 * 5 + 7b * 5) + 4) + -50 -122 + 25b = 7((-30 + 35b) + 4) + -50 Reorder the terms: -122 + 25b = 7(-30 + 4 + 35b) + -50 Combine like terms: -30 + 4 = -26 -122 + 25b = 7(-26 + 35b) + -50 -122 + 25b = (-26 * 7 + 35b * 7) + -50 -122 + 25b = (-182 + 245b) + -50 Reorder the terms: -122 + 25b = -182 + -50 + 245b Combine like terms: -182 + -50 = -232 -122 + 25b = -232 + 245b Solving -122 + 25b = -232 + 245b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-245b' to each side of the equation. -122 + 25b + -245b = -232 + 245b + -245b Combine like terms: 25b + -245b = -220b -122 + -220b = -232 + 245b + -245b Combine like terms: 245b + -245b = 0 -122 + -220b = -232 + 0 -122 + -220b = -232 Add '122' to each side of the equation. -122 + 122 + -220b = -232 + 122 Combine like terms: -122 + 122 = 0 0 + -220b = -232 + 122 -220b = -232 + 122 Combine like terms: -232 + 122 = -110 -220b = -110 Divide each side by '-220'. b = 0.5 Simplifying b = 0.5
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