Solve the Inequality for x 7^(3x+2)<=49^x

$7^{3 x + 2} \leq 49^{x}$

Step 1

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

$7^{3 x + 2} \leq 7^{2 x}$

Step 2

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

$3 x + 2 \leq 2 x$

Step 3

Solve for $x$ .

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

Subtract $2 x$ from both sides of the inequality.

$3 x + 2 - 2 x \leq 0$

Subtract $2 x$ from $3 x$ .

$x + 2 \leq 0$

Subtract $2$ from both sides of the inequality.

$x \leq - 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 2$

Interval Notation:

$(- \infty, - 2]$

Step 5