Answer :
To solve an equation of the form \(\frac{x}{a} = b\), we need to isolate \(x\). Here’s a step-by-step breakdown of the solution process:
1. Understand the given equation:
[tex]\[ \frac{x}{a} = b \][/tex]
This equation states that when \(x\) is divided by \(a\), the result is \(b\).
2. Identify the goal:
We want to solve for \(x\). This means we need to get \(x\) by itself on one side of the equation.
3. Determine the correct operation:
To isolate \(x\), we need to undo the division by \(a\). To do this, we perform the inverse operation of division, which is multiplication. Specifically, we multiply both sides of the equation by \(a\).
4. Apply the operation:
[tex]\[ \left(\frac{x}{a}\right) \cdot a = b \cdot a \][/tex]
On the left-hand side, \(\frac{x}{a} \cdot a\) simplifies to \(x\) because the \(a\) in the numerator and denominator cancel each other out.
5. Simplify the equation:
[tex]\[ x = b \cdot a \][/tex]
By following these steps, we see that the correct strategy is to multiply both sides by \(a\) to solve for \(x\). Therefore, the correct answer is D. multiply both sides by a:
[tex]\[ \boxed{\text{D}} \][/tex]
1. Understand the given equation:
[tex]\[ \frac{x}{a} = b \][/tex]
This equation states that when \(x\) is divided by \(a\), the result is \(b\).
2. Identify the goal:
We want to solve for \(x\). This means we need to get \(x\) by itself on one side of the equation.
3. Determine the correct operation:
To isolate \(x\), we need to undo the division by \(a\). To do this, we perform the inverse operation of division, which is multiplication. Specifically, we multiply both sides of the equation by \(a\).
4. Apply the operation:
[tex]\[ \left(\frac{x}{a}\right) \cdot a = b \cdot a \][/tex]
On the left-hand side, \(\frac{x}{a} \cdot a\) simplifies to \(x\) because the \(a\) in the numerator and denominator cancel each other out.
5. Simplify the equation:
[tex]\[ x = b \cdot a \][/tex]
By following these steps, we see that the correct strategy is to multiply both sides by \(a\) to solve for \(x\). Therefore, the correct answer is D. multiply both sides by a:
[tex]\[ \boxed{\text{D}} \][/tex]
