Solve for x 3/2(2x+4)=x+19

$\frac{3}{2} (2 x + 4) = x + 19$

Step 1

Simplify $\frac{3}{2} \cdot (2 x + 4)$ .

Rewrite.

$0 + 0 + \frac{3}{2} \cdot (2 x + 4) = x + 19$

Simplify by adding zeros.

$\frac{3}{2} \cdot (2 x + 4) = x + 19$

Apply the distributive property.

$\frac{3}{2} (2 x) + \frac{3}{2} \cdot 4 = x + 19$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{3}{2} (2 (x)) + \frac{3}{2} \cdot 4 = x + 19$

Cancel the common factor.

$\frac{3}{2} (2 x) + \frac{3}{2} \cdot 4 = x + 19$

Rewrite the expression.

$3 x + \frac{3}{2} \cdot 4 = x + 19$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$3 x + \frac{3}{2} \cdot (2 (2)) = x + 19$

Cancel the common factor.

$3 x + \frac{3}{2} \cdot (2 \cdot 2) = x + 19$

Rewrite the expression.

$3 x + 3 \cdot 2 = x + 19$

Multiply $3$ by $2$ .

$3 x + 6 = x + 19$

Step 2

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

Subtract $x$ from both sides of the equation.

$3 x + 6 - x = 19$

Subtract $x$ from $3 x$ .

$2 x + 6 = 19$

Step 3

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

Subtract $6$ from both sides of the equation.

$2 x = 19 - 6$

Subtract $6$ from $19$ .

$2 x = 13$

Step 4

Divide each term in $2 x = 13$ by $2$ and simplify.

Divide each term in $2 x = 13$ by $2$ .

$\frac{2 x}{2} = \frac{13}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{13}{2}$

Divide $x$ by $1$ .

$x = \frac{13}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13}{2}$

Decimal Form:

$x = 6.5$

Mixed Number Form:

$x = 6 \frac{1}{2}$

Solve for x 3/2(2x+4)=x+19

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