Solve for x 7(3x+1)+8(2x-3)=4(3x-1)-7(x-4)

$7 (3 x + 1) + 8 (2 x - 3) = 4 (3 x - 1) - 7 (x - 4)$

Step 1

Simplify $7 (3 x + 1) + 8 (2 x - 3)$ .

Simplify each term.

Apply the distributive property.

$7 (3 x) + 7 \cdot 1 + 8 (2 x - 3) = 4 (3 x - 1) - 7 (x - 4)$

Multiply $3$ by $7$ .

$21 x + 7 \cdot 1 + 8 (2 x - 3) = 4 (3 x - 1) - 7 (x - 4)$

Multiply $7$ by $1$ .

$21 x + 7 + 8 (2 x - 3) = 4 (3 x - 1) - 7 (x - 4)$

Apply the distributive property.

$21 x + 7 + 8 (2 x) + 8 \cdot - 3 = 4 (3 x - 1) - 7 (x - 4)$

Multiply $2$ by $8$ .

$21 x + 7 + 16 x + 8 \cdot - 3 = 4 (3 x - 1) - 7 (x - 4)$

Multiply $8$ by $- 3$ .

$21 x + 7 + 16 x - 24 = 4 (3 x - 1) - 7 (x - 4)$

Simplify by adding terms.

Add $21 x$ and $16 x$ .

$37 x + 7 - 24 = 4 (3 x - 1) - 7 (x - 4)$

Subtract $24$ from $7$ .

$37 x - 17 = 4 (3 x - 1) - 7 (x - 4)$

Step 2

Simplify $4 (3 x - 1) - 7 (x - 4)$ .

Simplify each term.

Apply the distributive property.

$37 x - 17 = 4 (3 x) + 4 \cdot - 1 - 7 (x - 4)$

Multiply $3$ by $4$ .

$37 x - 17 = 12 x + 4 \cdot - 1 - 7 (x - 4)$

Multiply $4$ by $- 1$ .

$37 x - 17 = 12 x - 4 - 7 (x - 4)$

Apply the distributive property.

$37 x - 17 = 12 x - 4 - 7 x - 7 \cdot - 4$

Multiply $- 7$ by $- 4$ .

$37 x - 17 = 12 x - 4 - 7 x + 28$

Simplify by adding terms.

Subtract $7 x$ from $12 x$ .

$37 x - 17 = 5 x - 4 + 28$

Add $- 4$ and $28$ .

$37 x - 17 = 5 x + 24$

Step 3

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

Subtract $5 x$ from both sides of the equation.

$37 x - 17 - 5 x = 24$

Subtract $5 x$ from $37 x$ .

$32 x - 17 = 24$

Step 4

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

Add $17$ to both sides of the equation.

$32 x = 24 + 17$

Add $24$ and $17$ .

$32 x = 41$

Step 5

Divide each term in $32 x = 41$ by $32$ and simplify.

Divide each term in $32 x = 41$ by $32$ .

$\frac{32 x}{32} = \frac{41}{32}$

Simplify the left side.

Cancel the common factor of $32$ .

Cancel the common factor.

$\frac{32 x}{32} = \frac{41}{32}$

Divide $x$ by $1$ .

$x = \frac{41}{32}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{41}{32}$

Decimal Form:

$x = 1.28125$

Mixed Number Form:

$x = 1 \frac{9}{32}$

Solve for x 7(3x+1)+8(2x-3)=4(3x-1)-7(x-4)

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