To solve the equation 5/8(x-1/2)=10, the first step is to reverse the multiplication. What number should both sides be divided by? (1 point)
To reverse the multiplication, you should multiply both sides of the equation by the reciprocal of 5/8, which is 8/5. However, in this case, it is simpler to multiply both sides by the reciprocal of the coefficient 5/8, which is 8/5. When you multiply both sides of the equation by 8/5, you get:
8/5 * (5/8)(x-1/2) = 8/5 * 10
On the left side, the 5/8 and 8/5 cancel each other out, resulting in:
x-1/2 = 8/5 * 10
Simplifying the right side, you get:
x-1/2 = 80/5
So, the result after reversing the multiplication is:
x-1/2 = 16
To isolate x, you can add 1/2 to both sides of the equation:
x-1/2 + 1/2 = 16 + 1/2
Simplifying further, you get:
x = 16 + 1/2
Therefore, the solution to the equation 5/8(x-1/2)=10 is x = 33/2.
To solve the equation 4.72 (a - 6.56 = 10.4, the first step is to reverse the multiplication by dividing by 4.72. After dividing by 4.72,
what number should be added to both sides? (1 point)
After dividing both sides of the equation by 4.72, you should subtract 6.56 from both sides to isolate the variable.
To clarify, the equation is: 4.72(a - 6.56) = 10.4
First, divide both sides by 4.72:
(a - 6.56) = 10.4 / 4.72
Simplifying the right side, you get:
(a - 6.56) ≈ 2.20339
Now, to isolate the variable a, you should add 6.56 to both sides of the equation:
(a - 6.56) + 6.56 ≈ 2.20339 + 6.56
This simplifies to:
a ≈ 8.76339
Therefore, the number that should be added to both sides after dividing by 4.72 is 6.56.
What is the solution of the equation 8/9(x+1/2)=32/3 when solving for x? (1 point)
To find the solution for the equation 8/9(x+1/2)=32/3, we can follow these steps:
1. Multiply both sides of the equation by 9/8 to eliminate 8/9 from the left side:
(9/8) * (8/9) * (x + 1/2) = (32/3) * (9/8)
Simplifying:
(x + 1/2) = (96/24) = 4
2. Subtract 1/2 from both sides to isolate x:
(x + 1/2) - 1/2 = 4 - 1/2
Simplifying:
x = 3.5
Therefore, the solution for the equation 8/9(x+1/2)=32/3 is x = 3.5.
What is the solution of the equation 8/9(x+1/2)=32/3 when solving for x?
To solve the equation 8/9(x+1/2)=32/3 for x, we can follow these steps:
First, let's simplify the equation:
8/9(x+1/2) = 32/3
To eliminate the fraction, we can multiply both sides of the equation by 9/8:
(9/8) * (8/9(x+1/2)) = (9/8) * (32/3)
Simplifying:
(x+1/2) = 36/1
Next, we can subtract 1/2 from both sides of the equation to isolate x:
(x+1/2) - 1/2 = 36/1 - 1/2
Simplifying:
x = 35/2
Therefore, the solution for the equation 8/9(x+1/2)=32/3 when solving for x is x = 35/2.