Algebra Examples

p (x) = 2^{5 x + 1} - 8^{2 x - 3}

$p (x) = 2^{5 x + 1} - 8^{2 x - 3}$

Step 1

Set

2^{5 x + 1} - 8^{2 x - 3}

$2^{5 x + 1} - 8^{2 x - 3}$ equal to

0

$0$ .

2^{5 x + 1} - 8^{2 x - 3} = 0

$2^{5 x + 1} - 8^{2 x - 3} = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

Move

- 8^{2 x - 3}

$- 8^{2 x - 3}$ to the right side of the equation by adding it to both sides.

2^{5 x + 1} = 8^{2 x - 3}

$2^{5 x + 1} = 8^{2 x - 3}$

Step 2.2

Create equivalent expressions in the equation that all have equal bases.

2^{5 x + 1} = 2^{3 (2 x - 3)}

$2^{5 x + 1} = 2^{3 (2 x - 3)}$

Step 2.3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

5 x + 1 = 3 (2 x - 3)

$5 x + 1 = 3 (2 x - 3)$

Step 2.4

Solve for

x

$x$ .

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Step 2.4.1

Simplify

3 (2 x - 3)

$3 (2 x - 3)$ .

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Step 2.4.1.1

Rewrite.

5 x + 1 = 0 + 0 + 3 (2 x - 3)

$5 x + 1 = 0 + 0 + 3 (2 x - 3)$

Step 2.4.1.2

Simplify by adding zeros.

5 x + 1 = 3 (2 x - 3)

$5 x + 1 = 3 (2 x - 3)$

Step 2.4.1.3

Apply the distributive property.

5 x + 1 = 3 (2 x) + 3 \cdot - 3

$5 x + 1 = 3 (2 x) + 3 \cdot - 3$

Step 2.4.1.4

Multiply.

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Step 2.4.1.4.1

Multiply

2

$2$ by

3

$3$ .

5 x + 1 = 6 x + 3 \cdot - 3

$5 x + 1 = 6 x + 3 \cdot - 3$

Step 2.4.1.4.2

Multiply

3

$3$ by

- 3

$- 3$ .

5 x + 1 = 6 x - 9

$5 x + 1 = 6 x - 9$

5 x + 1 = 6 x - 9

$5 x + 1 = 6 x - 9$

5 x + 1 = 6 x - 9

$5 x + 1 = 6 x - 9$

Step 2.4.2

Move all terms containing

x

$x$ to the left side of the equation.

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Step 2.4.2.1

Subtract

6 x

$6 x$ from both sides of the equation.

5 x + 1 - 6 x = - 9

$5 x + 1 - 6 x = - 9$

Step 2.4.2.2

Subtract

6 x

$6 x$ from

5 x

$5 x$ .

- x + 1 = - 9

$- x + 1 = - 9$

- x + 1 = - 9

$- x + 1 = - 9$

Step 2.4.3

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 2.4.3.1

Subtract

1

$1$ from both sides of the equation.

- x = - 9 - 1

$- x = - 9 - 1$

Step 2.4.3.2

Subtract

1

$1$ from

- 9

$- 9$ .

- x = - 10

$- x = - 10$

- x = - 10

$- x = - 10$

Step 2.4.4

Divide each term in

- x = - 10

$- x = - 10$ by

- 1

$- 1$ and simplify.

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Step 2.4.4.1

Divide each term in

- x = - 10

$- x = - 10$ by

- 1

$- 1$ .

\frac{- x}{- 1} = \frac{- 10}{- 1}

$\frac{- x}{- 1} = \frac{- 10}{- 1}$

Step 2.4.4.2

Simplify the left side.

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Step 2.4.4.2.1

Dividing two negative values results in a positive value.

\frac{x}{1} = \frac{- 10}{- 1}

$\frac{x}{1} = \frac{- 10}{- 1}$

Step 2.4.4.2.2

Divide

x

$x$ by

1

$1$ .

x = \frac{- 10}{- 1}

$x = \frac{- 10}{- 1}$

x = \frac{- 10}{- 1}

$x = \frac{- 10}{- 1}$

Step 2.4.4.3

Simplify the right side.

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Step 2.4.4.3.1

Divide

- 10

$- 10$ by

- 1

$- 1$ .

x = 10

$x = 10$

x = 10

$x = 10$

x = 10

$x = 10$

x = 10

$x = 10$

x = 10

$x = 10$

Step 3