Answer :
Certainly! Let's tackle the problem step-by-step.
### Part (a): Isolating the Variable
To solve the equation [tex]\(6x = 42\)[/tex] for [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex]. This can be done by performing operations that "cancel out" the number attached to [tex]\(x\)[/tex], which in this case is 6.
- Multiplying by [tex]\(1/6\)[/tex]:
- If you multiply both sides of the equation [tex]\(6x = 42\)[/tex] by [tex]\(1/6\)[/tex], it helps isolate [tex]\(x\)[/tex].
- Calculation: [tex]\( (1/6) \times 6x = (1/6) \times 42 \)[/tex].
- This simplifies to [tex]\(x = 42/6\)[/tex].
- Dividing by 6:
- If you divide both sides of the equation by 6, it also isolates [tex]\(x\)[/tex].
- Calculation: [tex]\(6x/6 = 42/6\)[/tex].
- This simplifies directly to [tex]\(x = 42/6\)[/tex].
Therefore, the operations that can isolate [tex]\(x\)[/tex] are:
- B. Multiplying by [tex]\(1/6\)[/tex]
- E. Dividing by 6
### Part (b): Solving the Equation
Now that we've decided on the operations to isolate [tex]\(x\)[/tex], let's find the solution.
Given [tex]\(6x = 42\)[/tex], dividing both sides by 6 (or multiplying by [tex]\(1/6\)[/tex]) gives us:
[tex]\[ x = \frac{42}{6} \][/tex]
By performing this division:
[tex]\[ x = 7 \][/tex]
Thus, the solution to the equation [tex]\(6x = 42\)[/tex] is:
[tex]\[ x = 7 \][/tex]
I hope this explanation clarifies the solution steps for you! Feel free to ask if you have any more questions.
### Part (a): Isolating the Variable
To solve the equation [tex]\(6x = 42\)[/tex] for [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex]. This can be done by performing operations that "cancel out" the number attached to [tex]\(x\)[/tex], which in this case is 6.
- Multiplying by [tex]\(1/6\)[/tex]:
- If you multiply both sides of the equation [tex]\(6x = 42\)[/tex] by [tex]\(1/6\)[/tex], it helps isolate [tex]\(x\)[/tex].
- Calculation: [tex]\( (1/6) \times 6x = (1/6) \times 42 \)[/tex].
- This simplifies to [tex]\(x = 42/6\)[/tex].
- Dividing by 6:
- If you divide both sides of the equation by 6, it also isolates [tex]\(x\)[/tex].
- Calculation: [tex]\(6x/6 = 42/6\)[/tex].
- This simplifies directly to [tex]\(x = 42/6\)[/tex].
Therefore, the operations that can isolate [tex]\(x\)[/tex] are:
- B. Multiplying by [tex]\(1/6\)[/tex]
- E. Dividing by 6
### Part (b): Solving the Equation
Now that we've decided on the operations to isolate [tex]\(x\)[/tex], let's find the solution.
Given [tex]\(6x = 42\)[/tex], dividing both sides by 6 (or multiplying by [tex]\(1/6\)[/tex]) gives us:
[tex]\[ x = \frac{42}{6} \][/tex]
By performing this division:
[tex]\[ x = 7 \][/tex]
Thus, the solution to the equation [tex]\(6x = 42\)[/tex] is:
[tex]\[ x = 7 \][/tex]
I hope this explanation clarifies the solution steps for you! Feel free to ask if you have any more questions.
