Finite Math Examples

$5 + 3 \cdot 2^{x} = 53$

Step 1

Subtract $53$ from both sides of the equation.

$5 + 3 \cdot 2^{x} - 53 = 0$

Step 2

Subtract $53$ from $5$ .

$3 \cdot 2^{x} - 48 = 0$

Step 3

Factor $3$ out of $3 \cdot 2^{x} - 48$ .

Tap for more steps...

Step 3.1

Factor $3$ out of $3 \cdot 2^{x}$ .

$3 (2^{x}) - 48 = 0$

Step 3.2

Factor $3$ out of $- 48$ .

$3 \cdot 2^{x} + 3 \cdot - 16 = 0$

Step 3.3

Factor $3$ out of $3 \cdot 2^{x} + 3 \cdot - 16$ .

$3 (2^{x} - 16) = 0$

Step 4

Divide each term in $3 (2^{x} - 16) = 0$ by $3$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $3 (2^{x} - 16) = 0$ by $3$ .

$\frac{3 (2^{x} - 16)}{3} = \frac{0}{3}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{3 (2^{x} - 16)}{3} = \frac{0}{3}$

Step 4.2.1.2

Divide $2^{x} - 16$ by $1$ .

$2^{x} - 16 = \frac{0}{3}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $0$ by $3$ .

$2^{x} - 16 = 0$

Step 5

Add $16$ to both sides of the equation.

$2^{x} = 16$

Step 6

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

$2^{x} = 2^{4}$

Step 7

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

$x = 4$