Algebra Examples

$\frac{7}{4 x + 3} = 2$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$4 x + 3, 1$

Step 1.2

Remove parentheses.

$4 x + 3, 1$

Step 1.3

The LCM of one and any expression is the expression.

$4 x + 3$

Step 2

Multiply each term in $\frac{7}{4 x + 3} = 2$ by $4 x + 3$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{7}{4 x + 3} = 2$ by $4 x + 3$ .

$\frac{7}{4 x + 3} (4 x + 3) = 2 (4 x + 3)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4 x + 3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{7}{4 x + 3} (4 x + 3) = 2 (4 x + 3)$

Step 2.2.1.2

Rewrite the expression.

$7 = 2 (4 x + 3)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$7 = 2 (4 x) + 2 \cdot 3$

Step 2.3.2

Multiply.

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Step 2.3.2.1

Multiply $4$ by $2$ .

$7 = 8 x + 2 \cdot 3$

Step 2.3.2.2

Multiply $2$ by $3$ .

$7 = 8 x + 6$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as $8 x + 6 = 7$ .

$8 x + 6 = 7$

Step 3.2

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

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Step 3.2.1

Subtract $6$ from both sides of the equation.

$8 x = 7 - 6$

Step 3.2.2

Subtract $6$ from $7$ .

$8 x = 1$

Step 3.3

Divide each term in $8 x = 1$ by $8$ and simplify.

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Step 3.3.1

Divide each term in $8 x = 1$ by $8$ .

$\frac{8 x}{8} = \frac{1}{8}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $8$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{1}{8}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{8}$

Decimal Form:

$x = 0.125$