To solve the equation [tex]\(\frac{x}{4} + 5 = 23\)[/tex], various properties of equality are applied in each step. Let's break down each step to understand these properties.
Step 1: [tex]\(\frac{x}{4} + 5 = 23\)[/tex]
This is the original equation given.
Step 2: [tex]\(\frac{x}{4} + 5 - 5 = 23 - 5\)[/tex]
Here, 5 is subtracted from both sides of the equation. The property of equality applied in this step is the subtraction property of equality, which states that if you subtract the same number from both sides of an equation, the equality remains the same.
Step 3: [tex]\(\frac{x}{4} = 18\)[/tex]
After simplifying, we get [tex]\(\frac{x}{4}\)[/tex] on the left side and 18 on the right side. This is the result of the previous subtraction.
Step 4: [tex]\(4 \cdot \frac{x}{4} = 4 \cdot 18\)[/tex]
At this step, both sides of the equation are multiplied by 4. The property of equality applied here is the multiplication property of equality, which states that if you multiply both sides of an equation by the same non-zero number, the equality remains valid.
Step 5: [tex]\(x = 72\)[/tex]
After simplifying, we get [tex]\(x = 72\)[/tex].
To complete the statements based on the table:
- In step 2, the subtraction property of equality was applied.
- In step 4, the multiplication property of equality was applied.
