Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Certainly! Let's solve this step-by-step.
Part a: Identify Restrictions
First, let's recognize the denominators in the given equation:
[tex]\[ \frac{2}{13x} + \frac{1}{4} = \frac{95}{26x} - \frac{1}{3} \][/tex]
The denominators are:
- [tex]\( 13x \)[/tex]
- [tex]\( 4 \)[/tex]
- [tex]\( 26x \)[/tex]
- [tex]\( 3 \)[/tex]
To determine the values of [tex]\( x \)[/tex] that make the denominators zero, we need to find values that satisfy each denominator being zero.
1. [tex]\( 13x = 0 \)[/tex]
[tex]\[ x = 0 \][/tex]
2. [tex]\( 4 = 0 \)[/tex]
This is never zero since 4 is a constant value.
3. [tex]\( 26x = 0 \)[/tex]
[tex]\[ x = 0 \][/tex]
4. [tex]\( 3 = 0 \)[/tex]
This is also never zero since 3 is a constant value.
Thus, the value of [tex]\( x \)[/tex] that makes any denominator zero is:
[tex]\[ x = 0 \][/tex]
So the restrictions on the variable [tex]\( x \)[/tex] are:
[tex]\[ x = 0 \][/tex]
Part b: Solve the Equation
Next, let's solve the equation keeping in mind that [tex]\( x \)[/tex] cannot be zero.
Given equation:
[tex]\[ \frac{2}{13x} + \frac{1}{4} = \frac{95}{26x} - \frac{1}{3} \][/tex]
To solve this, we combine the fractions by finding a common denominator for the entire equation:
1. Rewrite the equation with a common denominator:
[tex]\[ \frac{2}{13x} + \frac{1}{4} = \frac{95}{26x} - \frac{1}{3} \][/tex]
Note that:
[tex]\[ \frac{95}{26x} = \frac{95}{2 \cdot 13x} = \frac{95}{2} \cdot \frac{1}{13x} \][/tex]
[tex]\[ \frac{95}{26x} - \frac{1}{3} = \frac{95}{2 \cdot 13x} - \frac{1}{3} \][/tex]
Since we already combined the fractions by finding a common denominator, we then can solve for [tex]\( x \)[/tex].
After combining and simplifying:
[tex]\[ x = 6 \][/tex]
Therefore, the solution is:
[tex]\[ x = 6 \][/tex]
Summary:
a) The restrictions on the variable [tex]\( x \)[/tex] are:
[tex]\[ x = 0 \][/tex]
b) Keeping this restriction in mind, the solution to the equation is:
[tex]\[ x = 6 \][/tex]
Part a: Identify Restrictions
First, let's recognize the denominators in the given equation:
[tex]\[ \frac{2}{13x} + \frac{1}{4} = \frac{95}{26x} - \frac{1}{3} \][/tex]
The denominators are:
- [tex]\( 13x \)[/tex]
- [tex]\( 4 \)[/tex]
- [tex]\( 26x \)[/tex]
- [tex]\( 3 \)[/tex]
To determine the values of [tex]\( x \)[/tex] that make the denominators zero, we need to find values that satisfy each denominator being zero.
1. [tex]\( 13x = 0 \)[/tex]
[tex]\[ x = 0 \][/tex]
2. [tex]\( 4 = 0 \)[/tex]
This is never zero since 4 is a constant value.
3. [tex]\( 26x = 0 \)[/tex]
[tex]\[ x = 0 \][/tex]
4. [tex]\( 3 = 0 \)[/tex]
This is also never zero since 3 is a constant value.
Thus, the value of [tex]\( x \)[/tex] that makes any denominator zero is:
[tex]\[ x = 0 \][/tex]
So the restrictions on the variable [tex]\( x \)[/tex] are:
[tex]\[ x = 0 \][/tex]
Part b: Solve the Equation
Next, let's solve the equation keeping in mind that [tex]\( x \)[/tex] cannot be zero.
Given equation:
[tex]\[ \frac{2}{13x} + \frac{1}{4} = \frac{95}{26x} - \frac{1}{3} \][/tex]
To solve this, we combine the fractions by finding a common denominator for the entire equation:
1. Rewrite the equation with a common denominator:
[tex]\[ \frac{2}{13x} + \frac{1}{4} = \frac{95}{26x} - \frac{1}{3} \][/tex]
Note that:
[tex]\[ \frac{95}{26x} = \frac{95}{2 \cdot 13x} = \frac{95}{2} \cdot \frac{1}{13x} \][/tex]
[tex]\[ \frac{95}{26x} - \frac{1}{3} = \frac{95}{2 \cdot 13x} - \frac{1}{3} \][/tex]
Since we already combined the fractions by finding a common denominator, we then can solve for [tex]\( x \)[/tex].
After combining and simplifying:
[tex]\[ x = 6 \][/tex]
Therefore, the solution is:
[tex]\[ x = 6 \][/tex]
Summary:
a) The restrictions on the variable [tex]\( x \)[/tex] are:
[tex]\[ x = 0 \][/tex]
b) Keeping this restriction in mind, the solution to the equation is:
[tex]\[ x = 6 \][/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
