Solve for x 6(x+5)=7(x-(3-x))

$6 (x + 5) = 7 (x - (3 - x))$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$7 (x - (3 - x)) = 6 (x + 5)$

Step 2

Simplify $7 (x - (3 - x))$ .

Rewrite.

$0 + 0 + 7 (x - (3 - x)) = 6 (x + 5)$

Simplify by adding zeros.

$7 (x - (3 - x)) = 6 (x + 5)$

Simplify each term.

Apply the distributive property.

$7 (x - 1 \cdot 3 - - x) = 6 (x + 5)$

Multiply $- 1$ by $3$ .

$7 (x - 3 - - x) = 6 (x + 5)$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$7 (x - 3 + 1 x) = 6 (x + 5)$

Multiply $x$ by $1$ .

$7 (x - 3 + x) = 6 (x + 5)$

Simplify terms.

Add $x$ and $x$ .

$7 (2 x - 3) = 6 (x + 5)$

Apply the distributive property.

$7 (2 x) + 7 \cdot - 3 = 6 (x + 5)$

Multiply.

Multiply $2$ by $7$ .

$14 x + 7 \cdot - 3 = 6 (x + 5)$

Multiply $7$ by $- 3$ .

$14 x - 21 = 6 (x + 5)$

Step 3

Simplify $6 (x + 5)$ .

Apply the distributive property.

$14 x - 21 = 6 x + 6 \cdot 5$

Multiply $6$ by $5$ .

$14 x - 21 = 6 x + 30$

Step 4

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

Subtract $6 x$ from both sides of the equation.

$14 x - 21 - 6 x = 30$

Subtract $6 x$ from $14 x$ .

$8 x - 21 = 30$

Step 5

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

Add $21$ to both sides of the equation.

$8 x = 30 + 21$

Add $30$ and $21$ .

$8 x = 51$

Step 6

Divide each term in $8 x = 51$ by $8$ and simplify.

Divide each term in $8 x = 51$ by $8$ .

$\frac{8 x}{8} = \frac{51}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{51}{8}$

Divide $x$ by $1$ .

$x = \frac{51}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{51}{8}$

Decimal Form:

$x = 6.375$

Mixed Number Form:

$x = 6 \frac{3}{8}$

Solve for x 6(x+5)=7(x-(3-x))

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