Solve.
11y + 3y - (-18y + 2y) = 30
First, we simplify the expression inside the parentheses: - (-18y + 2y) = -(-16y) = 16y.
Now, we substitute this value back into the original equation:
11y + 3y + 16y = 30
Combining like terms, we get:
30y = 30
To solve for y, we divide both sides of the equation by 30:
y = 1.
Therefore, the solution is y = 1.
Evaluate the expression 5a x (6b + a) for a = 2 and b = 4.
To evaluate the expression 5a x (6b + a) for a = 2 and b = 4, we substitute these values into the expression:
5(2) x (6(4) + 2)
First, we simplify the expression inside the parentheses:
5(2) x (24 + 2)
Next, we simplify further:
10 x 26
Finally, we multiply to get the final answer:
260
Therefore, when a = 2 and b = 4, the expression 5a x (6b + a) evaluates to 260.
Solve.
-21x = -63
To solve the equation -21x = -63, we need to isolate the variable x.
We can do this by dividing both sides of the equation by -21:
-21x / -21 = -63 / -21
This simplifies to:
x = 3
Therefore, the solution to the equation -21x = -63 is x = 3.
Evaluate the expression -2r + r/4 for r = -12.
To evaluate the expression -2r + r/4 for r = -12, we substitute this value into the expression:
-2(-12) + (-12)/4
First, we simplify the multiplication and division:
24 + (-3)
Next, we add the two terms:
21
Therefore, when r = -12, the expression -2r + r/4 evaluates to 21.
Identify which expression is equivalent to 5a + b - 3c + 13a - 13b + 3c?
A) 16/3a + 1/3b
B) 2 - 1/3b
C) 16/3a + 2/3b
D) 16/3a - 2/3b
Using the commutative property of addition, we can rearrange the terms in the expression:
5a + b - 3c + 13a - 13b + 3c
Combining like terms, we get:
(5a + 13a) + (b - 13b) + (-3c + 3c)
This simplifies to:
18a - 12b
Therefore, the expression 5a + b - 3c + 13a - 13b + 3c is equivalent to 18a - 12b.
None of the given options (A, B, C, or D) match the expression 18a - 12b.
Identify which expression is equivalent to 5a + b - 3c + 1/3a - 1/3b + 3c?
A) 16/3a + 1/3b
B) 2 - 1/3b
C) 16/3a + 2/3b
D) 16/3a - 2/3b