Solve for x 4/7(21/8x+1/2)=-2(1/7-5/28x)

$\frac{4}{7} (\frac{21}{8} x + \frac{1}{2}) = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 1

Simplify $\frac{4}{7} \cdot (\frac{21}{8} x + \frac{1}{2})$ .

Start simplifying.

$0 + 0 + \frac{4}{7} \cdot (\frac{21}{8} x + \frac{1}{2}) = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Simplify by adding zeros.

$\frac{4}{7} \cdot (\frac{21}{8} x + \frac{1}{2}) = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Combine $\frac{21}{8}$ and $x$ .

$\frac{4}{7} \cdot (\frac{21 x}{8} + \frac{1}{2}) = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Apply the distributive property.

$\frac{4}{7} \cdot \frac{21 x}{8} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{4}{7} \cdot \frac{21 x}{4 (2)} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Cancel the common factor.

$\frac{4}{7} \cdot \frac{21 x}{4 \cdot 2} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Rewrite the expression.

$\frac{1}{7} \cdot \frac{21 x}{2} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Cancel the common factor of $7$ .

Factor $7$ out of $21 x$ .

$\frac{1}{7} \cdot \frac{7 (3 x)}{2} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Cancel the common factor.

$\frac{1}{7} \cdot \frac{7 (3 x)}{2} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Rewrite the expression.

$\frac{3 x}{2} + \frac{4}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3 x}{2} + \frac{2 (2)}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Cancel the common factor.

$\frac{3 x}{2} + \frac{2 \cdot 2}{7} \cdot \frac{1}{2} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Rewrite the expression.

$\frac{3 x}{2} + \frac{2}{7} = - 2 (\frac{1}{7} - \frac{5}{28} x)$

Step 2

Simplify $- 2 (\frac{1}{7} - \frac{5}{28} x)$ .

Simplify each term.

Combine $x$ and $\frac{5}{28}$ .

$\frac{3 x}{2} + \frac{2}{7} = - 2 (\frac{1}{7} - \frac{x \cdot 5}{28})$

Move $5$ to the left of $x$ .

$\frac{3 x}{2} + \frac{2}{7} = - 2 (\frac{1}{7} - \frac{5 x}{28})$

Simplify terms.

Apply the distributive property.

$\frac{3 x}{2} + \frac{2}{7} = - 2 (\frac{1}{7}) - 2 (- \frac{5 x}{28})$

Combine $- 2$ and $\frac{1}{7}$ .

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} - 2 (- \frac{5 x}{28})$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 x}{28}$ into the numerator.

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} - 2 \frac{- 5 x}{28}$

Factor $2$ out of $- 2$ .

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} + 2 (- 1) \frac{- 5 x}{28}$

Factor $2$ out of $28$ .

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} + 2 \cdot - 1 \frac{- 5 x}{2 \cdot 14}$

Cancel the common factor.

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} + 2 \cdot - 1 \frac{- 5 x}{2 \cdot 14}$

Rewrite the expression.

$\frac{3 x}{2} + \frac{2}{7} = \frac{- 2}{7} - 1 \frac{- 5 x}{14}$

Simplify each term.

Move the negative in front of the fraction.

$\frac{3 x}{2} + \frac{2}{7} = - \frac{2}{7} - 1 \frac{- 5 x}{14}$

Move the negative in front of the fraction.

$\frac{3 x}{2} + \frac{2}{7} = - \frac{2}{7} - 1 (- \frac{(5) x}{14})$

Multiply $- 1 (- \frac{5 x}{14})$ .

Multiply $- 1$ by $- 1$ .

$\frac{3 x}{2} + \frac{2}{7} = - \frac{2}{7} + 1 \frac{5 x}{14}$

Multiply $\frac{5 x}{14}$ by $1$ .

$\frac{3 x}{2} + \frac{2}{7} = - \frac{2}{7} + \frac{5 x}{14}$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $\frac{5 x}{14}$ from both sides of the equation.

$\frac{3 x}{2} + \frac{2}{7} - \frac{5 x}{14} = - \frac{2}{7}$

To write $\frac{3 x}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3 x}{2} \cdot \frac{7}{7} - \frac{5 x}{14} + \frac{2}{7} = - \frac{2}{7}$

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x}{2}$ by $\frac{7}{7}$ .

$\frac{3 x \cdot 7}{2 \cdot 7} - \frac{5 x}{14} + \frac{2}{7} = - \frac{2}{7}$

Multiply $2$ by $7$ .

$\frac{3 x \cdot 7}{14} - \frac{5 x}{14} + \frac{2}{7} = - \frac{2}{7}$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 7 - 5 x}{14} + \frac{2}{7} = - \frac{2}{7}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $3 x \cdot 7 - 5 x$ .

Factor $x$ out of $3 x \cdot 7$ .

$\frac{x (3 \cdot 7) - 5 x}{14} + \frac{2}{7} = - \frac{2}{7}$

Factor $x$ out of $- 5 x$ .

$\frac{x (3 \cdot 7) + x \cdot - 5}{14} + \frac{2}{7} = - \frac{2}{7}$

Factor $x$ out of $x (3 \cdot 7) + x \cdot - 5$ .

$\frac{x (3 \cdot 7 - 5)}{14} + \frac{2}{7} = - \frac{2}{7}$

Multiply $3$ by $7$ .

$\frac{x (21 - 5)}{14} + \frac{2}{7} = - \frac{2}{7}$

Subtract $5$ from $21$ .

$\frac{x \cdot 16}{14} + \frac{2}{7} = - \frac{2}{7}$

Cancel the common factor of $16$ and $14$ .

Factor $2$ out of $x \cdot 16$ .

$\frac{2 (x \cdot 8)}{14} + \frac{2}{7} = - \frac{2}{7}$

Cancel the common factors.

Factor $2$ out of $14$ .

$\frac{2 (x \cdot 8)}{2 (7)} + \frac{2}{7} = - \frac{2}{7}$

Cancel the common factor.

$\frac{2 (x \cdot 8)}{2 \cdot 7} + \frac{2}{7} = - \frac{2}{7}$

Rewrite the expression.

$\frac{x \cdot 8}{7} + \frac{2}{7} = - \frac{2}{7}$

Move $8$ to the left of $x$ .

$\frac{8 x}{7} + \frac{2}{7} = - \frac{2}{7}$

Step 4

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

Subtract $\frac{2}{7}$ from both sides of the equation.

$\frac{8 x}{7} = - \frac{2}{7} - \frac{2}{7}$

Combine the numerators over the common denominator.

$\frac{8 x}{7} = \frac{- 2 - 2}{7}$

Subtract $2$ from $- 2$ .

$\frac{8 x}{7} = \frac{- 4}{7}$

Move the negative in front of the fraction.

$\frac{8 x}{7} = - \frac{4}{7}$

Step 5

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

$8 x = - 4$

Step 6

Divide each term in $8 x = - 4$ by $8$ and simplify.

Divide each term in $8 x = - 4$ by $8$ .

$\frac{8 x}{8} = \frac{- 4}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 4}{8}$

Divide $x$ by $1$ .

$x = \frac{- 4}{8}$

Simplify the right side.

Cancel the common factor of $- 4$ and $8$ .

Factor $4$ out of $- 4$ .

$x = \frac{4 (- 1)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$x = \frac{4 \cdot - 1}{4 \cdot 2}$

Cancel the common factor.

$x = \frac{4 \cdot - 1}{4 \cdot 2}$

Rewrite the expression.

$x = \frac{- 1}{2}$

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}$

Decimal Form:

$x = - 0.5$

Solve for x 4/7(21/8x+1/2)=-2(1/7-5/28x)

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