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Simplifying h(x) = 4x + 3h(x + 4) + 7 Multiply h * x hx = 4x + 3h(x + 4) + 7 Reorder the terms: hx = 4x + 3h(4 + x) + 7 hx = 4x + (4 * 3h + x * 3h) + 7 hx = 4x + (12h + 3hx) + 7 Reorder the terms: hx = 7 + 12h + 3hx + 4x Solving hx = 7 + 12h + 3hx + 4x Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-12h' to each side of the equation. -12h + hx = 7 + 12h + 3hx + -12h + 4x Reorder the terms: -12h + hx = 7 + 12h + -12h + 3hx + 4x Combine like terms: 12h + -12h = 0 -12h + hx = 7 + 0 + 3hx + 4x -12h + hx = 7 + 3hx + 4x Add '-3hx' to each side of the equation. -12h + hx + -3hx = 7 + 3hx + -3hx + 4x Combine like terms: hx + -3hx = -2hx -12h + -2hx = 7 + 3hx + -3hx + 4x Combine like terms: 3hx + -3hx = 0 -12h + -2hx = 7 + 0 + 4x -12h + -2hx = 7 + 4x Reorder the terms: -7 + -12h + -2hx + -4x = 7 + 4x + -7 + -4x Reorder the terms: -7 + -12h + -2hx + -4x = 7 + -7 + 4x + -4x Combine like terms: 7 + -7 = 0 -7 + -12h + -2hx + -4x = 0 + 4x + -4x -7 + -12h + -2hx + -4x = 4x + -4x Combine like terms: 4x + -4x = 0 -7 + -12h + -2hx + -4x = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 12h + 2hx + 4x) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 12h + 2hx + 4x)' equal to zero and attempt to solve: Simplifying 7 + 12h + 2hx + 4x = 0 Solving 7 + 12h + 2hx + 4x = 0 Move all terms containing h to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + 12h + 2hx + -7 + 4x = 0 + -7 Reorder the terms: 7 + -7 + 12h + 2hx + 4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 12h + 2hx + 4x = 0 + -7 12h + 2hx + 4x = 0 + -7 Combine like terms: 0 + -7 = -7 12h + 2hx + 4x = -7 Add '-4x' to each side of the equation. 12h + 2hx + 4x + -4x = -7 + -4x Combine like terms: 4x + -4x = 0 12h + 2hx + 0 = -7 + -4x 12h + 2hx = -7 + -4x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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