Math Problem Statement

−(5d + 8) = 3(8 ─ d)

Solution

To solve the equation (5d+8)=3(8d)- (5d + 8) = 3(8 - d), follow these steps:

  1. Distribute the negative sign on the left-hand side: 5d8=3(8d)-5d - 8 = 3(8 - d)

  2. Distribute the 3 on the right-hand side: 5d8=243d-5d - 8 = 24 - 3d

  3. Move all terms involving dd to one side of the equation. Let's add 3d3d to both sides: 5d+3d8=24-5d + 3d - 8 = 24 Simplify: 2d8=24-2d - 8 = 24

  4. Move the constant term 8-8 to the other side by adding 8 to both sides: 2d=24+8-2d = 24 + 8 Simplify: 2d=32-2d = 32

  5. Solve for dd by dividing both sides by 2-2: d=322=16d = \frac{32}{-2} = -16

So, the solution is d=16d = -16.

Would you like more details on any of the steps, or do you have any other questions?


Here are 5 related questions for further practice:

  1. Solve the equation: 3(2x4)=5(x+2)3(2x - 4) = -5(x + 2).
  2. What is the value of yy in the equation 4y7=3(2y+1)4y - 7 = 3(2y + 1)?
  3. Solve for zz in the equation 2(z+5)=43z-2(z + 5) = 4 - 3z.
  4. If 72t=5(t+1)7 - 2t = 5(t + 1), what is the value of tt?
  5. Solve the equation: 3(4a2)=5(2a)-3(4a - 2) = 5(2 - a).

Tip: When dealing with equations, always perform the same operation on both sides to maintain equality.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Distributive Property
Solving for Variables

Formulas

Distributive property: a(b + c) = ab + ac
Solving linear equations

Theorems

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Suitable Grade Level

Grades 6-8