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:
- Combine like terms inside the parentheses: .
- The expression on the left-hand side now becomes:
[ \text{[box]}(3x) - \text{[box]}x ] - The right-hand side is given as . So we need the left-hand side to equal .
- To match the , the second term in the left-hand side must be -5x. This suggests that the second box must be 5.
- To balance the equation, the first box should result in , which means the first box must be -2.
Thus, the completed equation is:
Would you like further details or have any questions about this solution? Here are five related questions:
- What are the steps to combine like terms in algebraic expressions?
- How do you distribute a coefficient across a sum inside parentheses?
- Can you always solve for missing values in equations by comparing both sides?
- What would happen if the equation had additional terms involving ?
- 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