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Simplifying 7(2g + -5) + -4(g + -3) = 6(3g + 3) + -3(5g + -4) Reorder the terms: 7(-5 + 2g) + -4(g + -3) = 6(3g + 3) + -3(5g + -4) (-5 * 7 + 2g * 7) + -4(g + -3) = 6(3g + 3) + -3(5g + -4) (-35 + 14g) + -4(g + -3) = 6(3g + 3) + -3(5g + -4) Reorder the terms: -35 + 14g + -4(-3 + g) = 6(3g + 3) + -3(5g + -4) -35 + 14g + (-3 * -4 + g * -4) = 6(3g + 3) + -3(5g + -4) -35 + 14g + (12 + -4g) = 6(3g + 3) + -3(5g + -4) Reorder the terms: -35 + 12 + 14g + -4g = 6(3g + 3) + -3(5g + -4) Combine like terms: -35 + 12 = -23 -23 + 14g + -4g = 6(3g + 3) + -3(5g + -4) Combine like terms: 14g + -4g = 10g -23 + 10g = 6(3g + 3) + -3(5g + -4) Reorder the terms: -23 + 10g = 6(3 + 3g) + -3(5g + -4) -23 + 10g = (3 * 6 + 3g * 6) + -3(5g + -4) -23 + 10g = (18 + 18g) + -3(5g + -4) Reorder the terms: -23 + 10g = 18 + 18g + -3(-4 + 5g) -23 + 10g = 18 + 18g + (-4 * -3 + 5g * -3) -23 + 10g = 18 + 18g + (12 + -15g) Reorder the terms: -23 + 10g = 18 + 12 + 18g + -15g Combine like terms: 18 + 12 = 30 -23 + 10g = 30 + 18g + -15g Combine like terms: 18g + -15g = 3g -23 + 10g = 30 + 3g Solving -23 + 10g = 30 + 3g Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3g' to each side of the equation. -23 + 10g + -3g = 30 + 3g + -3g Combine like terms: 10g + -3g = 7g -23 + 7g = 30 + 3g + -3g Combine like terms: 3g + -3g = 0 -23 + 7g = 30 + 0 -23 + 7g = 30 Add '23' to each side of the equation. -23 + 23 + 7g = 30 + 23 Combine like terms: -23 + 23 = 0 0 + 7g = 30 + 23 7g = 30 + 23 Combine like terms: 30 + 23 = 53 7g = 53 Divide each side by '7'. g = 7.571428571 Simplifying g = 7.571428571
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