Math Problem Statement

2(5c+2)-2c=3(2c+3)+7

Solution

Let's solve the equation step by step:

Given equation:

2(5c+2)2c=3(2c+3)+72(5c + 2) - 2c = 3(2c + 3) + 7

Step 1: Expand both sides.

On the left-hand side: 2(5c+2)=10c+42(5c + 2) = 10c + 4 So: 10c+42c=3(2c+3)+710c + 4 - 2c = 3(2c + 3) + 7

On the right-hand side: 3(2c+3)=6c+93(2c + 3) = 6c + 9 So: 10c+42c=6c+9+710c + 4 - 2c = 6c + 9 + 7

Step 2: Simplify both sides.

Left-hand side: 10c2c+4=8c+410c - 2c + 4 = 8c + 4

Right-hand side: 6c+9+7=6c+166c + 9 + 7 = 6c + 16

Now the equation becomes: 8c+4=6c+168c + 4 = 6c + 16

Step 3: Move all the terms involving cc to one side.

Subtract 6c6c from both sides: 8c6c+4=168c - 6c + 4 = 16 2c+4=162c + 4 = 16

Step 4: Solve for cc.

Subtract 4 from both sides: 2c=1642c = 16 - 4 2c=122c = 12

Now, divide by 2: c=122=6c = \frac{12}{2} = 6

Final Answer:

c=6c = 6

Would you like any further details on the solution or any clarifications?

Here are some related questions for practice:

  1. Solve 3(4x1)+2x=5(x+2)3(4x - 1) + 2x = 5(x + 2).
  2. Solve 7(2d+1)4d=5(3d+4)7(2d + 1) - 4d = 5(3d + 4).
  3. Solve 4(3y2)6y=2(5y+3)+44(3y - 2) - 6y = 2(5y + 3) + 4.
  4. Solve 5(2b+3)+6b=7(b+4)+95(2b + 3) + 6b = 7(b + 4) + 9.
  5. Solve 6(a+4)3a=2(3a+5)+86(a + 4) - 3a = 2(3a + 5) + 8.

Tip: Always expand parentheses first and then simplify both sides before solving for the variable.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Distributive Property

Formulas

Distributive Property: a(b + c) = ab + ac

Theorems

Basic properties of equality (addition, subtraction, division)

Suitable Grade Level

Grades 6-8