Simplify 5a − 8c + b + 3c −9a + 6b.
Rearranging the terms, we have 5a - 9a + b + 6b - 8c + 3c.
Combining like terms, we have -4a + 7b - 5c.
Simplify −3/4r + 3 − 5/6r − 6
Combining like terms, we have -3/4r - 5/6r + 3 - 6.
To combine the fractions, we need a common denominator. The least common multiple of 4 and 6 is 12. Rewriting the fractions with a denominator of 12, we have -9/12r - 10/12r + 3 - 6.
Simplifying further, we have -19/12r - 3.
Expand 8(3p + 2).
To expand 8(3p + 2), we distribute the 8 to both terms inside the parentheses:
8 * 3p + 8 * 2
This simplifies to:
24p + 16
Expand −4(6a − 5).
To expand −4(6a − 5), we distribute the -4 to both terms inside the parentheses:
-4 * 6a + (-4) * (-5)
This simplifies to:
-24a + 20
Expand 7/4(8h+3).
To expand 7/4(8h + 3), we distribute the 7/4 to both terms inside the parentheses:
(7/4)(8h) + (7/4)(3)
This simplifies to:
(56h)/4 + 21/4
Further simplifying by dividing the numerators by the denominator:
14h + 21/4
Alternatively, we can express the fraction in mixed number form:
14h + 5 1/4
-5/6 (9b - 12)
To expand -5/6 (9b - 12), we distribute the -5/6 to both terms inside the parentheses:
(-5/6)(9b) + (-5/6)(-12)
This simplifies to:
-45b/6 + 60/6
Further simplifying by dividing the numerators by the denominator:
-15b + 10
Alternatively, we can express the fraction in mixed number form:
-15b + 1 4/6, which can be simplified to -15b + 1 2/3.