What value should replace the blank in the equation 6x …

Mathematics Questions

6x + ____ = 10 Please find the blank.

Short Answer

The process of solving the blank involves isolating it by subtracting 6x from both sides, resulting in the expression ____ = 10 – 6x. This can then be rewritten as either -6x + 10 or 10 – 6x, both of which are equivalent and correctly fill in the blank.

Step-by-Step Solution

Step 1: Isolate the Blank

To solve for the blank in the equation, we will begin by isolating it on one side. This is achieved by subtracting 6x from both sides of the equation. The equation will transform into: ____ = 10 – 6x. This step is crucial as it allows us to express the blank in terms of the remaining equation.

Step 2: Rewrite the Expression

Next, we need to analyze the expression we obtained after isolating the blank. The expression can be rewritten in different forms. We can express it as:

  • -6x + 10
  • 10 – 6x
. Both expressions are equivalent due to the commutative property of addition, meaning the order does not affect the sum.

Step 3: Fill in the Blank

Finally, we fill in the blank with the appropriate expression derived from our calculations. The blank should be filled with either -6x + 10 or 10 – 6x. Both options convey the same value and satisfy the original equation, allowing us to complete the equation accurately.

Related Concepts

Isolate The Blank

Defining the process of moving a variable or term to one side of an equation to solve for it

Commutative Property

Mathematical principle stating that the order of addition does not change the sum

Rewrite An Expression

The act of changing the form of an equation or expression while maintaining its equivalence.

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