Solve for x 4(3x+5+7(x+1))=7x+5

$4 (3 x + 5 + 7 (x + 1)) = 7 x + 5$

Step 1

Simplify $4 (3 x + 5 + 7 (x + 1))$ .

Rewrite.

$0 + 0 + 4 (3 x + 5 + 7 (x + 1)) = 7 x + 5$

Simplify by adding zeros.

$4 (3 x + 5 + 7 (x + 1)) = 7 x + 5$

Simplify each term.

Apply the distributive property.

$4 (3 x + 5 + 7 x + 7 \cdot 1) = 7 x + 5$

Multiply $7$ by $1$ .

$4 (3 x + 5 + 7 x + 7) = 7 x + 5$

Simplify terms.

Add $3 x$ and $7 x$ .

$4 (10 x + 5 + 7) = 7 x + 5$

Add $5$ and $7$ .

$4 (10 x + 12) = 7 x + 5$

Apply the distributive property.

$4 (10 x) + 4 \cdot 12 = 7 x + 5$

Multiply.

Multiply $10$ by $4$ .

$40 x + 4 \cdot 12 = 7 x + 5$

Multiply $4$ by $12$ .

$40 x + 48 = 7 x + 5$

Step 2

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

Subtract $7 x$ from both sides of the equation.

$40 x + 48 - 7 x = 5$

Subtract $7 x$ from $40 x$ .

$33 x + 48 = 5$

Step 3

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

Subtract $48$ from both sides of the equation.

$33 x = 5 - 48$

Subtract $48$ from $5$ .

$33 x = - 43$

Step 4

Divide each term in $33 x = - 43$ by $33$ and simplify.

Divide each term in $33 x = - 43$ by $33$ .

$\frac{33 x}{33} = \frac{- 43}{33}$

Simplify the left side.

Cancel the common factor of $33$ .

Cancel the common factor.

$\frac{33 x}{33} = \frac{- 43}{33}$

Divide $x$ by $1$ .

$x = \frac{- 43}{33}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{43}{33}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{43}{33}$

Decimal Form:

$x = - 1.\overline{30}$

Mixed Number Form:

$x = - 1 \frac{10}{33}$

Solve for x 4(3x+5+7(x+1))=7x+5

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