Math / Algebra

QuestionSolve for $x$ . $\frac{2 x}{5}-9=6$

Studdy Solution

STEP 1

1. The equation $\frac{2x}{5} - 9 = 6$ is asking us to solve for $x$ .
2. This is a linear equation with one variable and one solution.
3. The equation involves basic algebraic operations, specifically addition and multiplication.

STEP 2

1. Isolate the term containing $x$ .
2. Eliminate the fraction by multiplying.
3. Solve for $x$ .
4. Check the solution by substituting it back into the original equation.

STEP 3

Add 9 to both sides of the equation to isolate the term containing $x$ :
$\frac{2x}{5} - 9 + 9 = 6 + 9$
Simplify:
$\frac{2x}{5} = 15$

STEP 4

To eliminate the fraction, multiply both sides of the equation by 5:
$5 \times \frac{2x}{5} = 15 \times 5$
Simplify:
$2x = 75$

STEP 5

Divide both sides by 2 to solve for $x$ :
$x = \frac{75}{2}$
Simplify:
$x = 37.5$

STEP 6

Check the solution by substituting $x = 37.5$ back into the original equation:
$\frac{2(37.5)}{5} - 9 = 6$
Calculate:
$\frac{75}{5} - 9 = 6$
Simplify:
$15 - 9 = 6$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{37.5}$

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QuestionSolve for $x$ . $\frac{2 x}{5}-9=6$

Studdy Solution

STEP 1

1. The equation $\frac{2x}{5} - 9 = 6$ is asking us to solve for $x$ .
2. This is a linear equation with one variable and one solution.
3. The equation involves basic algebraic operations, specifically addition and multiplication.

STEP 2

1. Isolate the term containing $x$ .
2. Eliminate the fraction by multiplying.
3. Solve for $x$ .
4. Check the solution by substituting it back into the original equation.

STEP 3

Add 9 to both sides of the equation to isolate the term containing $x$ :
$\frac{2x}{5} - 9 + 9 = 6 + 9$
Simplify:
$\frac{2x}{5} = 15$

STEP 4

To eliminate the fraction, multiply both sides of the equation by 5:
$5 \times \frac{2x}{5} = 15 \times 5$
Simplify:
$2x = 75$

STEP 5

Divide both sides by 2 to solve for $x$ :
$x = \frac{75}{2}$
Simplify:
$x = 37.5$

STEP 6

Check the solution by substituting $x = 37.5$ back into the original equation:
$\frac{2(37.5)}{5} - 9 = 6$
Calculate:
$\frac{75}{5} - 9 = 6$
Simplify:
$15 - 9 = 6$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{37.5}$

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QuestionSolve for xxx. 2x5−9=6\frac{2 x}{5}-9=652x​−9=6

Studdy Solution

STEP 1

1. The equation 2x5−9=6\frac{2x}{5} - 9 = 652x​−9=6 is asking us to solve for xxx.2. This is a linear equation with one variable and one solution.3. The equation involves basic algebraic operations, specifically addition and multiplication.

STEP 2

1. Isolate the term containing xxx.2. Eliminate the fraction by multiplying.3. Solve for xxx.4. Check the solution by substituting it back into the original equation.

STEP 3

Add 9 to both sides of the equation to isolate the term containing xxx:2x5−9+9=6+9\frac{2x}{5} - 9 + 9 = 6 + 952x​−9+9=6+9Simplify:2x5=15\frac{2x}{5} = 1552x​=15

STEP 4

To eliminate the fraction, multiply both sides of the equation by 5:5×2x5=15×55 \times \frac{2x}{5} = 15 \times 55×52x​=15×5Simplify:2x=752x = 752x=75

STEP 5

Divide both sides by 2 to solve for xxx:x=752x = \frac{75}{2}x=275​Simplify:x=37.5x = 37.5x=37.5

STEP 6

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QuestionSolve for $x$ . $\frac{2 x}{5}-9=6$

1. The equation $\frac{2x}{5} - 9 = 6$ is asking us to solve for $x$ .
2. This is a linear equation with one variable and one solution.
3. The equation involves basic algebraic operations, specifically addition and multiplication.

1. Isolate the term containing $x$ .
2. Eliminate the fraction by multiplying.
3. Solve for $x$ .
4. Check the solution by substituting it back into the original equation.

Add 9 to both sides of the equation to isolate the term containing $x$ :
$\frac{2x}{5} - 9 + 9 = 6 + 9$
Simplify:
$\frac{2x}{5} = 15$

To eliminate the fraction, multiply both sides of the equation by 5:
$5 \times \frac{2x}{5} = 15 \times 5$
Simplify:
$2x = 75$

Divide both sides by 2 to solve for $x$ :
$x = \frac{75}{2}$
Simplify:
$x = 37.5$