Final answer:
In question a, we solve for the value of 'a' in the equation 3(a + 5) = 21. In question b, we simplify the expression 2(3x - 4) - 5. In question c, we apply the distributive property to 4(2x + 3).
Step-by-step explanation:
a) Solve for the value of 'a' in the equation 3(a + 5) = 21:
To solve for 'a', we can apply the distributive property by multiplying 3 by both 'a' and 5. This gives us 3a + 15 = 21. Next, we can subtract 15 from both sides of the equation to isolate 'a'. This gives us 3a = 6. Finally, we divide both sides of the equation by 3 to solve for 'a'. The solution is a = 2.
b) Simplify the expression 2(3x - 4) - 5:
To simplify this expression, we can start by applying the distributive property. We multiply 2 by both 3x and -4, which gives us 6x - 8. Next, we can subtract 5 from this expression to get the simplified form: 6x - 13.
c) Apply the distributive property to 4(2x + 3):
Applying the distributive property, we multiply 4 by both 2x and 3, which gives us 8x + 12.