Question

Hank needs to compare two expressions 1/2 (10x + 6) and -(3x + 10) +8 (x+1)

. He needs to know if one expression is greater than the other for all values of x. Which statement accurately describes the relationship between the two expressions?

Answer 1

To compare the two expressions, we can simplify and combine like terms.

For the first expression, 1/2 * (10x + 6), we distribute the 1/2 to each term inside the parentheses: (1/2) * 10x + (1/2) * 6 = 5x + 3.

For the second expression, -(3x + 10) + 8 (x+1), we can simplify by distributing the negative sign to the terms inside the parentheses: -3x - 10 + 8x + 8. Combining like terms, we get: 5x - 2.

So the two simplified expressions are 5x + 3 and 5x - 2.

To compare the two expressions for all values of x, we can keep the coefficients of x the same and compare the constant terms.

The constant term in the expression 5x + 3 is 3.
The constant term in the expression 5x - 2 is -2.

Since 3 is greater than -2, we can conclude that for all values of x, the expression 5x + 3 is greater than 5x - 2.

Therefore, the accurate relationship between the two expressions is that 5x + 3 > 5x - 2 for all values of x.