Solve for a 7(a+1)-3a=5+4(2a-1)

$7 (a + 1) - 3 a = 5 + 4 (2 a - 1)$

Step 1

Simplify $7 (a + 1) - 3 a$ .

Simplify each term.

Apply the distributive property.

$7 a + 7 \cdot 1 - 3 a = 5 + 4 (2 a - 1)$

Multiply $7$ by $1$ .

$7 a + 7 - 3 a = 5 + 4 (2 a - 1)$

Subtract $3 a$ from $7 a$ .

$4 a + 7 = 5 + 4 (2 a - 1)$

Step 2

Simplify $5 + 4 (2 a - 1)$ .

Simplify each term.

Apply the distributive property.

$4 a + 7 = 5 + 4 (2 a) + 4 \cdot - 1$

Multiply $2$ by $4$ .

$4 a + 7 = 5 + 8 a + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$4 a + 7 = 5 + 8 a - 4$

Subtract $4$ from $5$ .

$4 a + 7 = 8 a + 1$

Step 3

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

Subtract $8 a$ from both sides of the equation.

$4 a + 7 - 8 a = 1$

Subtract $8 a$ from $4 a$ .

$- 4 a + 7 = 1$

Step 4

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

Subtract $7$ from both sides of the equation.

$- 4 a = 1 - 7$

Subtract $7$ from $1$ .

$- 4 a = - 6$

Step 5

Divide each term in $- 4 a = - 6$ by $- 4$ and simplify.

Divide each term in $- 4 a = - 6$ by $- 4$ .

$\frac{- 4 a}{- 4} = \frac{- 6}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 a}{- 4} = \frac{- 6}{- 4}$

Divide $a$ by $1$ .

$a = \frac{- 6}{- 4}$

Simplify the right side.

Cancel the common factor of $- 6$ and $- 4$ .

Factor $- 2$ out of $- 6$ .

$a = \frac{- 2 (3)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$a = \frac{- 2 \cdot 3}{- 2 \cdot 2}$

Cancel the common factor.

$a = \frac{- 2 \cdot 3}{- 2 \cdot 2}$

Rewrite the expression.

$a = \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = \frac{3}{2}$

Decimal Form:

$a = 1.5$

Mixed Number Form:

$a = 1 \frac{1}{2}$

Solve for a 7(a+1)-3a=5+4(2a-1)

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