Algebra Examples

$3 (0.5 x - 4) = \frac{3}{2} x - 1.2$

Step 1

Simplify $3 (0.5 x - 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (0.5 x - 4) = \frac{3}{2} x - 1.2$

Step 1.2

Simplify by adding zeros.

$3 (0.5 x - 4) = \frac{3}{2} x - 1.2$

Step 1.3

Apply the distributive property.

$3 (0.5 x) + 3 \cdot - 4 = \frac{3}{2} x - 1.2$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $0.5$ by $3$ .

$1.5 x + 3 \cdot - 4 = \frac{3}{2} x - 1.2$

Step 1.4.2

Multiply $3$ by $- 4$ .

$1.5 x - 12 = \frac{3}{2} x - 1.2$

Step 2

Combine $\frac{3}{2}$ and $x$ .

$1.5 x - 12 = \frac{3 x}{2} - 1.2$

Step 3

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

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Step 3.1

Subtract $\frac{3 x}{2}$ from both sides of the equation.

$1.5 x - 12 - \frac{3 x}{2} = - 1.2$

Step 3.2

To write $1.5 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$1.5 x \cdot \frac{2}{2} - \frac{3 x}{2} - 12 = - 1.2$

Step 3.3

Combine $1.5 x$ and $\frac{2}{2}$ .

$\frac{1.5 x \cdot 2}{2} - \frac{3 x}{2} - 12 = - 1.2$

Step 3.4

Combine the numerators over the common denominator.

$\frac{1.5 x \cdot 2 - 3 x}{2} - 12 = - 1.2$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $1.5 x$ out of $1.5 x \cdot 2 - 3 x$ .

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Step 3.5.1.1.1

Move $x$ .

$\frac{1.5 \cdot 2 x - 3 x}{2} - 12 = - 1.2$

Step 3.5.1.1.2

Factor $1.5 x$ out of $1.5 \cdot 2 x$ .

$\frac{1.5 x (2) - 3 x}{2} - 12 = - 1.2$

Step 3.5.1.1.3

Factor $1.5 x$ out of $- 3 x$ .

$\frac{1.5 x (2) + 1.5 x (- 2)}{2} - 12 = - 1.2$

Step 3.5.1.1.4

Factor $1.5 x$ out of $1.5 x (2) + 1.5 x (- 2)$ .

$\frac{1.5 x (2 - 2)}{2} - 12 = - 1.2$

Step 3.5.1.2

Combine exponents.

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Step 3.5.1.2.1

Multiply $2 - 2$ by $1.5$ .

$\frac{0 x}{2} - 12 = - 1.2$

Step 3.5.1.2.2

Multiply $0$ by $x$ .

$\frac{0}{2} - 12 = - 1.2$

Step 3.5.2

Divide $0$ by $2$ .

$0 - 12 = - 1.2$

Step 3.6

Subtract $12$ from $0$ .

$- 12 = - 1.2$

Step 4

Since $- 12 \neq - 1.2$ , there are no solutions.

No solution