Question

Blake is simplifiying the expression 6-2x+5+4x. Here's his work.

6-2x+5+4x
(6-2)x + (5+4)x
4x+9x
13x
A. Blakes work is incorrect, explain why.
B. Write an expression equivalent to 6-2x+5+4x that has only 2 like terms.

Answer 1

Blake's simplification was incorrect because he did not properly combine like terms. The correct simplification of the expression 6-2x+5+4x is 11+2x, which combines the constants and the variable terms separately.

Step-by-step explanation:

Blake's work simplifying the expression 6-2x+5+4x is incorrect because he has incorrectly grouped the terms. The correct approach is to combine like terms, which involve combining the constant terms (numbers without variables) and the variable terms (terms with x) separately.

Correcting Blake's Work:

The original expression is 6-2x+5+4x. First, combine the constant terms:

6 + 5 = 11

Next, combine the variable terms:

-2x + 4x = 2x

Now, putting the constant and variable terms together, we get the simplified expression:

11 + 2x

This expression has only two like terms: one constant and one variable term.

Evaluating Reasonableness:

It's important to eliminate terms wherever possible to simplify the algebra and check to see if the simplified result is reasonable. In this case, the result of 11 + 2x is reasonable as it follows the proper algebraic convention of combining like terms.