The equation \( \frac{5}{b} = 10 \) can be rewritten as two equations joined by "and" as follows:
\( 5/b = 10 \) and \( b \neq 0 \).
\( 5/b = 10 \) and \( b \neq 0 \).
The value that completes the set of equations is x≠ ()
1. Start by isolating the fraction:
\[
\frac{15}{3x - 9} - 4 = 12
\]
Add \( 4 \) to both sides:
\[
\frac{15}{3x - 9} = 16
\]
2. Next, multiply both sides by \( 3x - 9 \) to eliminate the fraction (noting that \( 3x - 9 \neq 0 \)):
\[
15 = 16(3x - 9)
\]
Simplifying the right side:
\[
15 = 48x - 144
\]
3. Rearranging to solve for \( x \):
\[
48x = 15 + 144
\]
\[
48x = 159
\]
\[
x = \frac{159}{48}
\]
4. We also need to determine when \( 3x - 9 = 0 \) to find values to avoid:
\[
3x - 9 = 0 \implies 3x = 9 \implies x = 3
\]
Thus, the value that completes the set of equations is \( x \neq 3 \).
The final answer is:
\( x \neq 3 \)
The undefined value is()
\[
22 = \frac{4 + 5x}{9x - 6}
\]
we should identify when the denominator is equal to zero, as this would make the expression undefined.
Set the denominator equal to zero:
\[
9x - 6 = 0
\]
Now, solve for \( x \):
\[
9x = 6
\]
\[
x = \frac{6}{9}
\]
Now, simplify the fraction:
\[
x = \frac{2}{3}
\]
Therefore, the undefined value is
\[
\frac{2}{3}
\]
Thus, the final answer is:
The undefined value is \( \frac{2}{3} \).
x=()
1. Subtract \( 4 \) from both sides:
\[
1x = 2 - 4
\]
\[
1x = -2
\]
2. Divide both sides by \( 1 \):
\[
x = -2
\]
Thus, the solution for \( x \) is:
\[
x = -2
\]
x=()
\[
\frac{1}{x} + 4 = 2,
\]
follow these steps:
1. Subtract \( 4 \) from both sides:
\[
\frac{1}{x} = 2 - 4
\]
\[
\frac{1}{x} = -2.
\]
2. Now, take the reciprocal of both sides to solve for \( x \):
\[
x = \frac{1}{-2} = -\frac{1}{2}.
\]
Therefore, the solution for \( x \) is:
\[
x = -\frac{1}{2}.
\]
p=()
\[
\frac{17}{p} + 4 = 55,
\]
follow these steps:
1. Subtract \( 4 \) from both sides:
\[
\frac{17}{p} = 55 - 4
\]
\[
\frac{17}{p} = 51.
\]
2. Now, multiply both sides by \( p \) to eliminate the fraction:
\[
17 = 51p.
\]
3. Next, divide both sides by \( 51 \) to solve for \( p \):
\[
p = \frac{17}{51}.
\]
4. Now, simplify the fraction:
\[
p = \frac{1}{3} \quad \text{(since both 17 and 51 can be divided by 17)}.
\]
Thus, the value of \( p \) is
\[
p = \frac{1}{3}.
\]