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?
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.