Let's solve the equation step by step to fill in the blanks correctly.
-
Start with the equation: \[ 45x - 5 = \frac{1}{4} \]
-
Add 5 to both sides of the equation: \[ 45x = \frac{1}{4} + 5 \] To work with this correctly, convert 5 to a fraction: \[ 5 = \frac{20}{4} \] Now, we can add: \[ \frac{1}{4} + \frac{20}{4} = \frac{21}{4} \] Thus, \[ 45x = \frac{21}{4} \]
-
Now, divide both sides by 45: \[ x = \frac{21}{4 \cdot 45} \] Multiply the denominators: \[ 4 \cdot 45 = 180 \] Therefore, \[ x = \frac{21}{180} \] This fraction can be simplified:
The greatest common divisor (GCD) of 21 and 180 is 3: \[ x = \frac{21 \div 3}{180 \div 3} = \frac{7}{60} \]
Now, we can fill in the blanks appropriately:
-
First Blank (after the first equation): \[ \frac{21}{4} \]
-
Second Blank (final value of \( x \)): \[ \frac{7}{60} \]
So the complete solution entries are:
- 45x = \(\frac{21}{4}\)
- x = \(\frac{7}{60}\)