Algebra Examples

$3 (x + 3 (4 x - 5)) = 15 x - 24$

Step 1

Simplify $3 (x + 3 (4 x - 5))$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (x + 3 (4 x - 5)) = 15 x - 24$

Step 1.2

Simplify by adding zeros.

$3 (x + 3 (4 x - 5)) = 15 x - 24$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$3 (x + 3 (4 x) + 3 \cdot - 5) = 15 x - 24$

Step 1.3.2

Multiply $4$ by $3$ .

$3 (x + 12 x + 3 \cdot - 5) = 15 x - 24$

Step 1.3.3

Multiply $3$ by $- 5$ .

$3 (x + 12 x - 15) = 15 x - 24$

$3 (x + 12 x - 15) = 15 x - 24$

Step 1.4

Simplify terms.

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Step 1.4.1

Add $x$ and $12 x$ .

$3 (13 x - 15) = 15 x - 24$

Step 1.4.2

Apply the distributive property.

$3 (13 x) + 3 \cdot - 15 = 15 x - 24$

Step 1.4.3

Multiply.

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Step 1.4.3.1

Multiply $13$ by $3$ .

$39 x + 3 \cdot - 15 = 15 x - 24$

Step 1.4.3.2

Multiply $3$ by $- 15$ .

$39 x - 45 = 15 x - 24$

$39 x - 45 = 15 x - 24$

$39 x - 45 = 15 x - 24$

$39 x - 45 = 15 x - 24$

Step 2

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

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Step 2.1

Subtract $15 x$ from both sides of the equation.

$39 x - 45 - 15 x = - 24$

Step 2.2

Subtract $15 x$ from $39 x$ .

$24 x - 45 = - 24$

$24 x - 45 = - 24$

Step 3

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

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Step 3.1

Add $45$ to both sides of the equation.

$24 x = - 24 + 45$

Step 3.2

Add $- 24$ and $45$ .

$24 x = 21$

$24 x = 21$

Step 4

Divide each term in $24 x = 21$ by $24$ and simplify.

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Step 4.1

Divide each term in $24 x = 21$ by $24$ .

$\frac{24 x}{24} = \frac{21}{24}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $24$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{24 x}{24} = \frac{21}{24}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{21}{24}$

$x = \frac{21}{24}$

$x = \frac{21}{24}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $21$ and $24$ .

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Step 4.3.1.1

Factor $3$ out of $21$ .

$x = \frac{3 (7)}{24}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $3$ out of $24$ .

$x = \frac{3 \cdot 7}{3 \cdot 8}$

Step 4.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 7}{3 \cdot 8}$

Step 4.3.1.2.3

Rewrite the expression.

$x = \frac{7}{8}$

$x = \frac{7}{8}$

$x = \frac{7}{8}$

$x = \frac{7}{8}$

$x = \frac{7}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{8}$

Decimal Form:

$x = 0.875$

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