ADD AND SUBTRACT ALGEBRAIC EXPRESSIONS PRACTICE

Question

COMPLETE THIS ASSESSMENT TO REVIEW WHAT YOU'VE LEARNED. IT WILL NOT COUNT TOWARD YOUR GRADE.

Add:1/2 (x+4)+ 1/4 (4x-2). The answer should be in mixed number form

Answer 1

To solve this expression, we need to first distribute the fractions to their respective terms:

1/2 (x+4) = 1/2 * x + 1/2 * 4 = 1/2x + 2/2 = 1/2x + 1
1/4 (4x-2) = 1/4 * 4x + 1/4 * (-2) = 4/4x - 2/4 = x - 1/2

Now, we can add the two expressions:

(1/2x + 1) + (x - 1/2)

To combine like terms, we need to find a common denominator for the fractions:

The least common multiple of 2 and 4 is 4. So, we can rewrite the expression as:

(1/2x + 1) + (x - 2/4)

Now, to add the fractions, they must have a common denominator. We can convert 1 to 2/2:

(1/2x + 2/2) + (x - 2/4)

Simplifying further:

(1/2x + 2/2) + (x - 1/2)

Now, we combine the like terms:

1/2x + 2/2 + x - 1/2

To simplify, we need to find a common denominator again:

The least common multiple of 2 and 2 is 2. So, we can rewrite the expression as:

1/2x + 2/2 + 2x/2 - 1/2

Combining like terms:

(1/2x + 2x/2) + (2/2 - 1/2)

Simplifying:

1/2x + x/2 + 1/2

To add the fractions with a common denominator:

(1/2x + x/2) + 1/2

Now, we add the numerators:

(1x + x^2)/2x + 1/2

Combining the terms:

(x + x^2)/2x + 1/2

This is the final expression in mixed number form.