Math Problem Statement

Write the missing values to complete this statement: [ ](x + 2x) - [ ]x = 2a + 5x

Solution

The question you uploaded is asking to find the missing values to complete the equation. Here's the expression:

[ \text{[box]}(x + 2x) - \text{[box]}x = 2a + 5x ]

We need to fill in the two boxes on the left-hand side of the equation so that it matches the right-hand side.

Step-by-step solution:

  1. Combine like terms inside the parentheses: x+2x=3xx + 2x = 3x.
  2. The expression on the left-hand side now becomes:
    [ \text{[box]}(3x) - \text{[box]}x ]
  3. The right-hand side is given as 2a+5x2a + 5x. So we need the left-hand side to equal 2a+5x2a + 5x.
  4. To match the 5x5x, the second term in the left-hand side must be -5x. This suggests that the second box must be 5.
  5. To balance the equation, the first box should result in 3x5x=2x3x - 5x = -2x, which means the first box must be -2.

Thus, the completed equation is:

2(3x)5x=2a+5x-2(3x) - 5x = 2a + 5x

Would you like further details or have any questions about this solution? Here are five related questions:

  1. What are the steps to combine like terms in algebraic expressions?
  2. How do you distribute a coefficient across a sum inside parentheses?
  3. Can you always solve for missing values in equations by comparing both sides?
  4. What would happen if the equation had additional terms involving aa?
  5. How can you check if a solution is correct by substitution?

Tip: When solving algebraic equations, always simplify each side as much as possible before trying to balance or solve for unknowns.

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Math Problem Analysis

Mathematical Concepts

Algebra
Combining Like Terms
Balancing Equations

Formulas

x + 2x = 3x
-2(3x) - 5x = 2a + 5x

Theorems

Basic Algebraic Manipulation
Distributive Property

Suitable Grade Level

Grades 8-10