Answer :
Sure! Let's go through each part of the question step by step.
### Part 1: Solving the Equation [tex]\(\frac{60}{4} = \frac{4x}{4}\)[/tex]
1. Simplify Both Sides:
- The left side of the equation is [tex]\(\frac{60}{4}\)[/tex], which simplifies to 15.
- The right side of the equation is [tex]\(\frac{4x}{4}\)[/tex]. Since the 4s cancel each other out, this simplifies to [tex]\(x\)[/tex].
2. Set the Simplified Forms Equal:
- After simplification, the equation becomes:
[tex]\[
15 = x
\][/tex]
3. Conclusion:
- The solution for this part is [tex]\(x = 15\)[/tex].
### Part 2: Solving the Equation [tex]\(4\sqrt{3} - 12 = 1\sqrt{3}\)[/tex]
1. Combine Like Terms:
- Start by isolating the terms with [tex]\(\sqrt{3}\)[/tex] on one side:
[tex]\[
4\sqrt{3} - 1\sqrt{3} = 12
\][/tex]
- This simplifies to:
[tex]\[
3\sqrt{3} = 12
\][/tex]
2. Solve for [tex]\(\sqrt{3}\)[/tex]:
- To solve for [tex]\(\sqrt{3}\)[/tex], divide both sides by 3:
[tex]\[
\sqrt{3} = \frac{12}{3}
\][/tex]
- Simplifying this gives:
[tex]\[
\sqrt{3} = 4
\][/tex]
3. Conclusion:
- So, [tex]\(\sqrt{3} = 4\)[/tex].
Thus, we have two answers:
- For the first equation, [tex]\(x = 15\)[/tex].
- For the second equation, [tex]\(\sqrt{3} = 4\)[/tex].
### Part 1: Solving the Equation [tex]\(\frac{60}{4} = \frac{4x}{4}\)[/tex]
1. Simplify Both Sides:
- The left side of the equation is [tex]\(\frac{60}{4}\)[/tex], which simplifies to 15.
- The right side of the equation is [tex]\(\frac{4x}{4}\)[/tex]. Since the 4s cancel each other out, this simplifies to [tex]\(x\)[/tex].
2. Set the Simplified Forms Equal:
- After simplification, the equation becomes:
[tex]\[
15 = x
\][/tex]
3. Conclusion:
- The solution for this part is [tex]\(x = 15\)[/tex].
### Part 2: Solving the Equation [tex]\(4\sqrt{3} - 12 = 1\sqrt{3}\)[/tex]
1. Combine Like Terms:
- Start by isolating the terms with [tex]\(\sqrt{3}\)[/tex] on one side:
[tex]\[
4\sqrt{3} - 1\sqrt{3} = 12
\][/tex]
- This simplifies to:
[tex]\[
3\sqrt{3} = 12
\][/tex]
2. Solve for [tex]\(\sqrt{3}\)[/tex]:
- To solve for [tex]\(\sqrt{3}\)[/tex], divide both sides by 3:
[tex]\[
\sqrt{3} = \frac{12}{3}
\][/tex]
- Simplifying this gives:
[tex]\[
\sqrt{3} = 4
\][/tex]
3. Conclusion:
- So, [tex]\(\sqrt{3} = 4\)[/tex].
Thus, we have two answers:
- For the first equation, [tex]\(x = 15\)[/tex].
- For the second equation, [tex]\(\sqrt{3} = 4\)[/tex].
