Algebra Examples

$4 (2 r - 17) + 5 (3 r - 8) = 0$

Step 1

Simplify $4 (2 r - 17) + 5 (3 r - 8)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 (2 r) + 4 \cdot - 17 + 5 (3 r - 8) = 0$

Step 1.1.2

Multiply $2$ by $4$ .

$8 r + 4 \cdot - 17 + 5 (3 r - 8) = 0$

Step 1.1.3

Multiply $4$ by $- 17$ .

$8 r - 68 + 5 (3 r - 8) = 0$

Step 1.1.4

Apply the distributive property.

$8 r - 68 + 5 (3 r) + 5 \cdot - 8 = 0$

Step 1.1.5

Multiply $3$ by $5$ .

$8 r - 68 + 15 r + 5 \cdot - 8 = 0$

Step 1.1.6

Multiply $5$ by $- 8$ .

$8 r - 68 + 15 r - 40 = 0$

$8 r - 68 + 15 r - 40 = 0$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $8 r$ and $15 r$ .

$23 r - 68 - 40 = 0$

Step 1.2.2

Subtract $40$ from $- 68$ .

$23 r - 108 = 0$

$23 r - 108 = 0$

$23 r - 108 = 0$

Step 2

Add $108$ to both sides of the equation.

$23 r = 108$

Step 3

Divide each term in $23 r = 108$ by $23$ and simplify.

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Step 3.1

Divide each term in $23 r = 108$ by $23$ .

$\frac{23 r}{23} = \frac{108}{23}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $23$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{23 r}{23} = \frac{108}{23}$

Step 3.2.1.2

Divide $r$ by $1$ .

$r = \frac{108}{23}$

$r = \frac{108}{23}$

$r = \frac{108}{23}$

$r = \frac{108}{23}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$r = \frac{108}{23}$

Decimal Form:

$r = 4.69565217 \dots$

Mixed Number Form:

$r = 4 \frac{16}{23}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$