Algebra Examples

$\frac{2 x - 5.6}{3} = \frac{1 - x}{1.5}$

Step 1

Multiply both sides by $3$ .

$\frac{2 x - 5.6}{3} \cdot 3 = \frac{1 - x}{1.5} \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{2 x - 5.6}{3} \cdot 3$ .

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Step 2.1.1.1

Factor $0.4$ out of $2 x - 5.6$ .

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Step 2.1.1.1.1

Factor $0.4$ out of $2 x$ .

$\frac{0.4 (5 x) - 5.6}{3} \cdot 3 = \frac{1 - x}{1.5} \cdot 3$

Step 2.1.1.1.2

Factor $0.4$ out of $- 5.6$ .

$\frac{0.4 (5 x) + 0.4 (- 14)}{3} \cdot 3 = \frac{1 - x}{1.5} \cdot 3$

Step 2.1.1.1.3

Factor $0.4$ out of $0.4 (5 x) + 0.4 (- 14)$ .

$\frac{0.4 (5 x - 14)}{3} \cdot 3 = \frac{1 - x}{1.5} \cdot 3$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{0.4 (5 x - 14)}{3} \cdot 3 = \frac{1 - x}{1.5} \cdot 3$

Step 2.1.1.2.2

Rewrite the expression.

$0.4 (5 x - 14) = \frac{1 - x}{1.5} \cdot 3$

Step 2.1.1.3

Apply the distributive property.

$0.4 (5 x) + 0.4 \cdot - 14 = \frac{1 - x}{1.5} \cdot 3$

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $5$ by $0.4$ .

$2 x + 0.4 \cdot - 14 = \frac{1 - x}{1.5} \cdot 3$

Step 2.1.1.4.2

Multiply $0.4$ by $- 14$ .

$2 x - 5.6 = \frac{1 - x}{1.5} \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{1 - x}{1.5} \cdot 3$ .

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Step 2.2.1.1

Cancel the common factor of $1.5$ .

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Step 2.2.1.1.1

Factor $1.5$ out of $3$ .

$2 x - 5.6 = \frac{1 - x}{1.5} \cdot (1.5 (2))$

Step 2.2.1.1.2

Cancel the common factor.

$2 x - 5.6 = \frac{1 - x}{1.5} \cdot (1.5 \cdot 2)$

Step 2.2.1.1.3

Rewrite the expression.

$2 x - 5.6 = (1 - x) \cdot 2$

Step 2.2.1.2

Apply the distributive property.

$2 x - 5.6 = 1 \cdot 2 - x \cdot 2$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $2$ by $1$ .

$2 x - 5.6 = 2 - x \cdot 2$

Step 2.2.1.3.2

Multiply $2$ by $- 1$ .

$2 x - 5.6 = 2 - 2 x$

Step 2.2.1.3.3

Reorder $2$ and $- 2 x$ .

$2 x - 5.6 = - 2 x + 2$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $2 x$ to both sides of the equation.

$2 x - 5.6 + 2 x = 2$

Step 3.1.2

Add $2 x$ and $2 x$ .

$4 x - 5.6 = 2$

Step 3.2

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

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Step 3.2.1

Add $5.6$ to both sides of the equation.

$4 x = 2 + 5.6$

Step 3.2.2

Add $2$ and $5.6$ .

$4 x = 7.6$

Step 3.3

Divide each term in $4 x = 7.6$ by $4$ and simplify.

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Step 3.3.1

Divide each term in $4 x = 7.6$ by $4$ .

$\frac{4 x}{4} = \frac{7.6}{4}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $4$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{7.6}{4}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{7.6}{4}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $7.6$ by $4$ .

$x = 1.9$