5 answers
To solve the equation \( 4.72(x - 6.56) = 10.4 \), the first step is indeed to divide both sides by \( 4.72 \).
So, you divide:
\[ x - 6.56 = \frac{10.4}{4.72} \]
Calculating the right side:
\[ \frac{10.4}{4.72} \approx 2.207 \]
After this division, the equation simplifies to:
\[ x - 6.56 \approx 2.207 \]
Next, to isolate \( x \), you need to add \( 6.56 \) to both sides:
\[ x \approx 2.207 + 6.56 \]
So, the number that should be added to both sides is \( 6.56 \).
To solve the equation
\[ \frac{8}{9}(x + \frac{1}{2}) = \frac{32}{3}, \]
we can start by eliminating the fraction on the left side by multiplying both sides of the equation by \( \frac{9}{8} \):
\[ x + \frac{1}{2} = \frac{32}{3} \cdot \frac{9}{8}. \]
Now we calculate the right side:
\[ \frac{32}{3} \cdot \frac{9}{8} = \frac{32 \cdot 9}{3 \cdot 8} = \frac{288}{24} = 12. \]
Now we can substitute back into the equation:
\[ x + \frac{1}{2} = 12. \]
Next, we isolate \( x \) by subtracting \( \frac{1}{2} \) from both sides:
\[ x = 12 - \frac{1}{2} = 12 - 0.5 = 11.5. \]
Thus, the solution for \( x \) is
\[ \boxed{11.5}. \]
To solve the equation
\[ 6.24(x + 5.9) = 20.22, \]
the first step is to reverse the multiplication by dividing both sides by \( 6.24 \).
This gives:
\[ x + 5.9 = \frac{20.22}{6.24}. \]
So, the number that both sides should be divided by is
\[ \boxed{6.24}. \]
