Solve for a 43=|15-4a|

$43 = | 15 - 4 a |$

Rewrite the equation as $| 15 - 4 a | = 43$ .

$| 15 - 4 a | = 43$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$15 - 4 a = \pm 43$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$15 - 4 a = 43$

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

Subtract $15$ from both sides of the equation.

$- 4 a = 43 - 15$

Subtract $15$ from $43$ .

$- 4 a = 28$

Divide each term in $- 4 a = 28$ by $- 4$ and simplify.

Divide each term in $- 4 a = 28$ by $- 4$ .

$\frac{- 4 a}{- 4} = \frac{28}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 a}{- 4} = \frac{28}{- 4}$

Divide $a$ by $1$ .

$a = \frac{28}{- 4}$

Simplify the right side.

Divide $28$ by $- 4$ .

$a = - 7$

Next, use the negative value of the $\pm$ to find the second solution.

$15 - 4 a = - 43$

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

Subtract $15$ from both sides of the equation.

$- 4 a = - 43 - 15$

Subtract $15$ from $- 43$ .

$- 4 a = - 58$

Divide each term in $- 4 a = - 58$ by $- 4$ and simplify.

Divide each term in $- 4 a = - 58$ by $- 4$ .

$\frac{- 4 a}{- 4} = \frac{- 58}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 a}{- 4} = \frac{- 58}{- 4}$

Divide $a$ by $1$ .

$a = \frac{- 58}{- 4}$

Simplify the right side.

Cancel the common factor of $- 58$ and $- 4$ .

Factor $- 2$ out of $- 58$ .

$a = \frac{- 2 (29)}{- 4}$

Cancel the common factors.

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

$a = \frac{- 2 \cdot 29}{- 2 \cdot 2}$

Cancel the common factor.

$a = \frac{- 2 \cdot 29}{- 2 \cdot 2}$

Rewrite the expression.

$a = \frac{29}{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$a = - 7, \frac{29}{2}$

The result can be shown in multiple forms.

Exact Form:

$a = - 7, \frac{29}{2}$

Decimal Form:

$a = - 7, 14.5$

Mixed Number Form:

$a = - 7, 14 \frac{1}{2}$

Solve for a 43=|15-4a|

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