Algebra Examples

$1 = \frac{3 x}{4} + \frac{7}{4}$

Step 1

Rewrite the equation as $\frac{3 x}{4} + \frac{7}{4} = 1$ .

$\frac{3 x}{4} + \frac{7}{4} = 1$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Subtract $\frac{7}{4}$ from both sides of the equation.

$\frac{3 x}{4} = 1 - \frac{7}{4}$

Step 2.2

Write $1$ as a fraction with a common denominator.

$\frac{3 x}{4} = \frac{4}{4} - \frac{7}{4}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{3 x}{4} = \frac{4 - 7}{4}$

Step 2.4

Subtract $7$ from $4$ .

$\frac{3 x}{4} = \frac{- 3}{4}$

Step 2.5

Move the negative in front of the fraction.

$\frac{3 x}{4} = - \frac{3}{4}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 x = - 3$

Step 4

Divide each term in $3 x = - 3$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 x = - 3$ by $3$ .

$\frac{3 x}{3} = \frac{- 3}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 3}{3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 3$ by $3$ .

$x = - 1$