Question
Solve for x
in the following equation: 15/x+10+7=8
(
in the following equation: 15/x+10+7=8
(
Answers
GPT-4o mini
To solve the equation \( \frac{15}{x} + 10 + 7 = 8 \), we can follow these steps:
1. Combine like terms on the left side:
\[
\frac{15}{x} + 17 = 8
\]
2. Isolate the term \( \frac{15}{x} \) by subtracting 17 from both sides:
\[
\frac{15}{x} = 8 - 17
\]
\[
\frac{15}{x} = -9
\]
3. Now, we need to get \( x \) by multiplying both sides by \( x \) (assuming \( x \neq 0 \)):
\[
15 = -9x
\]
4. Solve for \( x \) by dividing both sides by -9:
\[
x = \frac{15}{-9}
\]
\[
x = -\frac{5}{3}
\]
Thus, the solution for \( x \) is:
\[
\boxed{-\frac{5}{3}}
\]
1. Combine like terms on the left side:
\[
\frac{15}{x} + 17 = 8
\]
2. Isolate the term \( \frac{15}{x} \) by subtracting 17 from both sides:
\[
\frac{15}{x} = 8 - 17
\]
\[
\frac{15}{x} = -9
\]
3. Now, we need to get \( x \) by multiplying both sides by \( x \) (assuming \( x \neq 0 \)):
\[
15 = -9x
\]
4. Solve for \( x \) by dividing both sides by -9:
\[
x = \frac{15}{-9}
\]
\[
x = -\frac{5}{3}
\]
Thus, the solution for \( x \) is:
\[
\boxed{-\frac{5}{3}}
\]
solve for x
GPT-4o mini
It seems you want to solve an equation for \( x \), but there isn't a specific equation provided in your latest message.
If you would like to solve the same equation as before, \( \frac{15}{x} + 10 + 7 = 8 \), we already found that:
\[
x = -\frac{5}{3}
\]
If you have a different equation in mind or would like me to help with another math problem, please provide the equation, and I'll assist you!
If you would like to solve the same equation as before, \( \frac{15}{x} + 10 + 7 = 8 \), we already found that:
\[
x = -\frac{5}{3}
\]
If you have a different equation in mind or would like me to help with another math problem, please provide the equation, and I'll assist you!
-5/3 is wrong
GPT-4o mini
Let’s solve the equation step-by-step again and check the calculations.
Given the equation:
\[
\frac{15}{x} + 10 + 7 = 8
\]
1. First, combine like terms:
\[
\frac{15}{x} + 17 = 8
\]
2. Now, subtract 17 from both sides:
\[
\frac{15}{x} = 8 - 17
\]
\[
\frac{15}{x} = -9
\]
3. Next, to eliminate the fraction, multiply both sides by \( x \) (assuming \( x \neq 0 \)):
\[
15 = -9x
\]
4. Now solve for \( x \) by dividing both sides by -9:
\[
x = \frac{15}{-9}
\]
\[
x = -\frac{5}{3}
\]
After going through the calculations again, the result remains:
\[
x = -\frac{5}{3}
\]
If there is something specific that might have been misinterpreted or if there’s another equation you want me to solve, please let me know!
Given the equation:
\[
\frac{15}{x} + 10 + 7 = 8
\]
1. First, combine like terms:
\[
\frac{15}{x} + 17 = 8
\]
2. Now, subtract 17 from both sides:
\[
\frac{15}{x} = 8 - 17
\]
\[
\frac{15}{x} = -9
\]
3. Next, to eliminate the fraction, multiply both sides by \( x \) (assuming \( x \neq 0 \)):
\[
15 = -9x
\]
4. Now solve for \( x \) by dividing both sides by -9:
\[
x = \frac{15}{-9}
\]
\[
x = -\frac{5}{3}
\]
After going through the calculations again, the result remains:
\[
x = -\frac{5}{3}
\]
If there is something specific that might have been misinterpreted or if there’s another equation you want me to solve, please let me know!
Using the properties of inequality, justify both steps in solving the inequality: 3/5 x + 6 ≥ 36
What is the solution to the inequality?(1 point)
What is the solution to the inequality?(1 point)
GPT-4o mini
To solve the inequality \( \frac{3}{5} x + 6 \geq 36 \), we'll apply properties of inequalities step by step and justify each step.
**Step 1:** Subtract 6 from both sides.
- **Justification:** Subtracting the same number from both sides of an inequality does not change the direction of the inequality.
\[
\frac{3}{5} x + 6 - 6 \geq 36 - 6
\]
This simplifies to:
\[
\frac{3}{5} x \geq 30
\]
**Step 2:** Multiply both sides by \( \frac{5}{3} \).
- **Justification:** Multiplying both sides of an inequality by a positive number does not change the direction of the inequality. (Note: It is important to confirm that the multiplier is positive).
\[
x \geq 30 \cdot \frac{5}{3}
\]
Calculating the right side:
\[
30 \cdot \frac{5}{3} = 10 \cdot 5 = 50
\]
So, we have:
\[
x \geq 50
\]
Thus, the solution to the inequality is:
\[
\boxed{x \geq 50}
\]
### Summary:
1. Subtracting 6 from both sides to isolate the term with \( x \).
2. Multiplying by \( \frac{5}{3} \) to solve for \( x \).
Both steps are justified based on properties of inequalities.
**Step 1:** Subtract 6 from both sides.
- **Justification:** Subtracting the same number from both sides of an inequality does not change the direction of the inequality.
\[
\frac{3}{5} x + 6 - 6 \geq 36 - 6
\]
This simplifies to:
\[
\frac{3}{5} x \geq 30
\]
**Step 2:** Multiply both sides by \( \frac{5}{3} \).
- **Justification:** Multiplying both sides of an inequality by a positive number does not change the direction of the inequality. (Note: It is important to confirm that the multiplier is positive).
\[
x \geq 30 \cdot \frac{5}{3}
\]
Calculating the right side:
\[
30 \cdot \frac{5}{3} = 10 \cdot 5 = 50
\]
So, we have:
\[
x \geq 50
\]
Thus, the solution to the inequality is:
\[
\boxed{x \geq 50}
\]
### Summary:
1. Subtracting 6 from both sides to isolate the term with \( x \).
2. Multiplying by \( \frac{5}{3} \) to solve for \( x \).
Both steps are justified based on properties of inequalities.