Math / Algebra

QuestionSolve the following rational equation. $5-\frac{4}{x}=7$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ \}. (Simplify your answer. Use a comma to separate answers as needed.) B. The solution is the empty set.

Studdy Solution

STEP 1

1. The equation $5 - \frac{4}{x} = 7$ is a rational equation.
2. We will solve for $x$ by isolating the variable term.

STEP 2

1. Isolate the rational term $\frac{4}{x}$ .
2. Solve for $x$ .
3. Check for any restrictions on the solution.

STEP 3

First, subtract 5 from both sides of the equation to isolate the rational term:
$5 - \frac{4}{x} = 7$ $-\frac{4}{x} = 7 - 5$ $-\frac{4}{x} = 2$

STEP 4

Multiply both sides by $-1$ to make the fraction positive:
$\frac{4}{x} = -2$

STEP 5

To solve for $x$ , multiply both sides by $x$ to eliminate the fraction:
$4 = -2x$

STEP 6

Now, divide both sides by $-2$ to solve for $x$ :
$x = \frac{4}{-2}$ $x = -2$

STEP 7

Check for any restrictions. Since $x$ cannot be zero (as it would make the denominator zero), and $x = -2$ does not violate this restriction, it is a valid solution.
The solution set is:
$\{-2\}$

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Studdy Solution

STEP 1

1. The equation $5 - \frac{4}{x} = 7$ is a rational equation.
2. We will solve for $x$ by isolating the variable term.

STEP 2

1. Isolate the rational term $\frac{4}{x}$ .
2. Solve for $x$ .
3. Check for any restrictions on the solution.

STEP 3

First, subtract 5 from both sides of the equation to isolate the rational term:
$5 - \frac{4}{x} = 7$ $-\frac{4}{x} = 7 - 5$ $-\frac{4}{x} = 2$

STEP 4

Multiply both sides by $-1$ to make the fraction positive:
$\frac{4}{x} = -2$

STEP 5

To solve for $x$ , multiply both sides by $x$ to eliminate the fraction:
$4 = -2x$

STEP 6

Now, divide both sides by $-2$ to solve for $x$ :
$x = \frac{4}{-2}$ $x = -2$

STEP 7

Check for any restrictions. Since $x$ cannot be zero (as it would make the denominator zero), and $x = -2$ does not violate this restriction, it is a valid solution.
The solution set is:
$\{-2\}$

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Studdy Solution

STEP 1

1. The equation 5−4x=7 5 - \frac{4}{x} = 7 5−x4​=7 is a rational equation.2. We will solve for x x x by isolating the variable term.

STEP 2

1. Isolate the rational term 4x \frac{4}{x} x4​.2. Solve for x x x.3. Check for any restrictions on the solution.

STEP 3

First, subtract 5 from both sides of the equation to isolate the rational term:5−4x=7 5 - \frac{4}{x} = 7 5−x4​=7 −4x=7−5 -\frac{4}{x} = 7 - 5 −x4​=7−5 −4x=2 -\frac{4}{x} = 2 −x4​=2

STEP 4

Multiply both sides by −1 -1 −1 to make the fraction positive:4x=−2 \frac{4}{x} = -2 x4​=−2

STEP 5

To solve for x x x, multiply both sides by x x x to eliminate the fraction:4=−2x 4 = -2x 4=−2x

STEP 6

Now, divide both sides by −2-2−2 to solve for x x x:x=4−2 x = \frac{4}{-2} x=−24​ x=−2 x = -2 x=−2

STEP 7

Check for any restrictions. Since x x x cannot be zero (as it would make the denominator zero), and x=−2 x = -2 x=−2 does not violate this restriction, it is a valid solution. The solution set is:{−2} \{-2\} {−2}

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1. The equation $5 - \frac{4}{x} = 7$ is a rational equation.
2. We will solve for $x$ by isolating the variable term.

1. Isolate the rational term $\frac{4}{x}$ .
2. Solve for $x$ .
3. Check for any restrictions on the solution.

First, subtract 5 from both sides of the equation to isolate the rational term:
$5 - \frac{4}{x} = 7$ $-\frac{4}{x} = 7 - 5$ $-\frac{4}{x} = 2$

Multiply both sides by $-1$ to make the fraction positive:
$\frac{4}{x} = -2$

To solve for $x$ , multiply both sides by $x$ to eliminate the fraction:
$4 = -2x$

Now, divide both sides by $-2$ to solve for $x$ :
$x = \frac{4}{-2}$ $x = -2$

Check for any restrictions. Since $x$ cannot be zero (as it would make the denominator zero), and $x = -2$ does not violate this restriction, it is a valid solution.
The solution set is:
$\{-2\}$