Solve for x 5(2x+1)+4=6(3x+2)+7

$5 (2 x + 1) + 4 = 6 (3 x + 2) + 7$

Step 1

Simplify $5 (2 x + 1) + 4$ .

Simplify each term.

Apply the distributive property.

$5 (2 x) + 5 \cdot 1 + 4 = 6 (3 x + 2) + 7$

Multiply $2$ by $5$ .

$10 x + 5 \cdot 1 + 4 = 6 (3 x + 2) + 7$

Multiply $5$ by $1$ .

$10 x + 5 + 4 = 6 (3 x + 2) + 7$

Add $5$ and $4$ .

$10 x + 9 = 6 (3 x + 2) + 7$

Step 2

Simplify $6 (3 x + 2) + 7$ .

Simplify each term.

Apply the distributive property.

$10 x + 9 = 6 (3 x) + 6 \cdot 2 + 7$

Multiply $3$ by $6$ .

$10 x + 9 = 18 x + 6 \cdot 2 + 7$

Multiply $6$ by $2$ .

$10 x + 9 = 18 x + 12 + 7$

Add $12$ and $7$ .

$10 x + 9 = 18 x + 19$

Step 3

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

Subtract $18 x$ from both sides of the equation.

$10 x + 9 - 18 x = 19$

Subtract $18 x$ from $10 x$ .

$- 8 x + 9 = 19$

Step 4

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

Subtract $9$ from both sides of the equation.

$- 8 x = 19 - 9$

Subtract $9$ from $19$ .

$- 8 x = 10$

Step 5

Divide each term in $- 8 x = 10$ by $- 8$ and simplify.

Divide each term in $- 8 x = 10$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{10}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{10}{- 8}$

Divide $x$ by $1$ .

$x = \frac{10}{- 8}$

Simplify the right side.

Cancel the common factor of $10$ and $- 8$ .

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{- 8}$

Cancel the common factors.

Factor $2$ out of $- 8$ .

$x = \frac{2 \cdot 5}{2 \cdot - 4}$

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot - 4}$

Rewrite the expression.

$x = \frac{5}{- 4}$

Move the negative in front of the fraction.

$x = - \frac{5}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5}{4}$

Decimal Form:

$x = - 1.25$

Mixed Number Form:

$x = - 1 \frac{1}{4}$

Solve for x 5(2x+1)+4=6(3x+2)+7

Related Questions

Support LCMGCF.com by disabling your adblocker.