Solve for x 3(x+4)=0.6(15x+5)-6

$3 (x + 4) = 0.6 (15 x + 5) - 6$

Step 1

Simplify $3 (x + 4)$ .

Rewrite.

$0 + 0 + 3 (x + 4) = 0.6 (15 x + 5) - 6$

Simplify by adding zeros.

$3 (x + 4) = 0.6 (15 x + 5) - 6$

Apply the distributive property.

$3 x + 3 \cdot 4 = 0.6 (15 x + 5) - 6$

Multiply $3$ by $4$ .

$3 x + 12 = 0.6 (15 x + 5) - 6$

Step 2

Simplify $0.6 (15 x + 5) - 6$ .

Simplify each term.

Apply the distributive property.

$3 x + 12 = 0.6 (15 x) + 0.6 \cdot 5 - 6$

Multiply $15$ by $0.6$ .

$3 x + 12 = 9 x + 0.6 \cdot 5 - 6$

Multiply $0.6$ by $5$ .

$3 x + 12 = 9 x + 3 - 6$

Subtract $6$ from $3$ .

$3 x + 12 = 9 x - 3$

Step 3

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

Subtract $9 x$ from both sides of the equation.

$3 x + 12 - 9 x = - 3$

Subtract $9 x$ from $3 x$ .

$- 6 x + 12 = - 3$

Step 4

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

Subtract $12$ from both sides of the equation.

$- 6 x = - 3 - 12$

Subtract $12$ from $- 3$ .

$- 6 x = - 15$

Step 5

Divide each term in $- 6 x = - 15$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 15$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 15}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 15}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 15}{- 6}$

Simplify the right side.

Cancel the common factor of $- 15$ and $- 6$ .

Factor $- 3$ out of $- 15$ .

$x = \frac{- 3 (5)}{- 6}$

Cancel the common factors.

Factor $- 3$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{5}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

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

Solve for x 3(x+4)=0.6(15x+5)-6

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