Solve the Inequality for x 3^(5x-1)<=27^(x+3)

$3^{5 x - 1} \leq 27^{x + 3}$

Step 1

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

$3^{5 x - 1} \leq 3^{3 (x + 3)}$

Step 2

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

$5 x - 1 \leq 3 (x + 3)$

Step 3

Solve for $x$ .

Simplify $3 (x + 3)$ .

Rewrite.

$5 x - 1 \leq 0 + 0 + 3 (x + 3)$

Simplify by adding zeros.

$5 x - 1 \leq 3 (x + 3)$

Apply the distributive property.

$5 x - 1 \leq 3 x + 3 \cdot 3$

Multiply $3$ by $3$ .

$5 x - 1 \leq 3 x + 9$

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

Subtract $3 x$ from both sides of the inequality.

$5 x - 1 - 3 x \leq 9$

Subtract $3 x$ from $5 x$ .

$2 x - 1 \leq 9$

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

Add $1$ to both sides of the inequality.

$2 x \leq 9 + 1$

Add $9$ and $1$ .

$2 x \leq 10$

Divide each term in $2 x \leq 10$ by $2$ and simplify.

Divide each term in $2 x \leq 10$ by $2$ .

$\frac{2 x}{2} \leq \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{10}{2}$

Divide $x$ by $1$ .

$x \leq \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x \leq 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 5$

Interval Notation:

$(- \infty, 5]$

Step 5

Solve the Inequality for x 3^(5x-1)<=27^(x+3)

Related Questions

Support LCMGCF.com by disabling your adblocker.