Solve for x (5x+1)/5+(4x)/7=34/35

$\frac{5 x + 1}{5} + \frac{4 x}{7} = \frac{34}{35}$

Simplify $\frac{5 x + 1}{5} + \frac{4 x}{7}$ .

To write $\frac{5 x + 1}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{5 x + 1}{5} \cdot \frac{7}{7} + \frac{4 x}{7} = \frac{34}{35}$

To write $\frac{4 x}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5 x + 1}{5} \cdot \frac{7}{7} + \frac{4 x}{7} \cdot \frac{5}{5} = \frac{34}{35}$

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 x + 1}{5}$ by $\frac{7}{7}$ .

$\frac{(5 x + 1) \cdot 7}{5 \cdot 7} + \frac{4 x}{7} \cdot \frac{5}{5} = \frac{34}{35}$

Multiply $5$ by $7$ .

$\frac{(5 x + 1) \cdot 7}{35} + \frac{4 x}{7} \cdot \frac{5}{5} = \frac{34}{35}$

Multiply $\frac{4 x}{7}$ by $\frac{5}{5}$ .

$\frac{(5 x + 1) \cdot 7}{35} + \frac{4 x \cdot 5}{7 \cdot 5} = \frac{34}{35}$

Multiply $7$ by $5$ .

$\frac{(5 x + 1) \cdot 7}{35} + \frac{4 x \cdot 5}{35} = \frac{34}{35}$

Combine the numerators over the common denominator.

$\frac{(5 x + 1) \cdot 7 + 4 x \cdot 5}{35} = \frac{34}{35}$

Simplify the numerator.

Apply the distributive property.

$\frac{5 x \cdot 7 + 1 \cdot 7 + 4 x \cdot 5}{35} = \frac{34}{35}$

Multiply $7$ by $5$ .

$\frac{35 x + 1 \cdot 7 + 4 x \cdot 5}{35} = \frac{34}{35}$

Multiply $7$ by $1$ .

$\frac{35 x + 7 + 4 x \cdot 5}{35} = \frac{34}{35}$

Multiply $5$ by $4$ .

$\frac{35 x + 7 + 20 x}{35} = \frac{34}{35}$

Add $35 x$ and $20 x$ .

$\frac{55 x + 7}{35} = \frac{34}{35}$

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

$55 x + 7 = 34$

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

Subtract $7$ from both sides of the equation.

$55 x = 34 - 7$

Subtract $7$ from $34$ .

$55 x = 27$

Divide each term in $55 x = 27$ by $55$ and simplify.

Divide each term in $55 x = 27$ by $55$ .

$\frac{55 x}{55} = \frac{27}{55}$

Simplify the left side.

Cancel the common factor of $55$ .

Cancel the common factor.

$\frac{55 x}{55} = \frac{27}{55}$

Divide $x$ by $1$ .

$x = \frac{27}{55}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{27}{55}$

Decimal Form:

$x = 0.4\overline{90}$

Solve for x (5x+1)/5+(4x)/7=34/35

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