Linear Algebra Examples

$\frac{1}{2} \cdot (2 a + 7) = \frac{3 a - 4}{4}$

Step 1

Simplify $\frac{1}{2} \cdot (2 a + 7)$ .

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Step 1.1

Apply the distributive property.

$\frac{1}{2} (2 a) + \frac{1}{2} \cdot 7 = \frac{3 a - 4}{4}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $2 a$ .

$\frac{1}{2} (2 (a)) + \frac{1}{2} \cdot 7 = \frac{3 a - 4}{4}$

Step 1.2.2

Cancel the common factor.

$\frac{1}{2} (2 a) + \frac{1}{2} \cdot 7 = \frac{3 a - 4}{4}$

Step 1.2.3

Rewrite the expression.

$a + \frac{1}{2} \cdot 7 = \frac{3 a - 4}{4}$

Step 1.3

Combine $\frac{1}{2}$ and $7$ .

$a + \frac{7}{2} = \frac{3 a - 4}{4}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$a \approx - 18$

Step 3