Solve the Inequality for x 7^(3x+4)<49^(2x+1)

$7^{3 x + 4} < 49^{2 x + 1}$

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

$7^{3 x + 4} < 7^{2 (2 x + 1)}$

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

$3 x + 4 < 2 (2 x + 1)$

Solve for $x$ .

Simplify $2 (2 x + 1)$ .

Rewrite.

$3 x + 4 < 0 + 0 + 2 (2 x + 1)$

Simplify by adding zeros.

$3 x + 4 < 2 (2 x + 1)$

Apply the distributive property.

$3 x + 4 < 2 (2 x) + 2 \cdot 1$

Multiply.

Multiply $2$ by $2$ .

$3 x + 4 < 4 x + 2 \cdot 1$

Multiply $2$ by $1$ .

$3 x + 4 < 4 x + 2$

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

Subtract $4 x$ from both sides of the inequality.

$3 x + 4 - 4 x < 2$

Subtract $4 x$ from $3 x$ .

$- x + 4 < 2$

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

Subtract $4$ from both sides of the inequality.

$- x < 2 - 4$

Subtract $4$ from $2$ .

$- x < - 2$

Divide each term in $- x < - 2$ by $- 1$ and simplify.

Divide each term in $- x < - 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x > \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x > 2$

The result can be shown in multiple forms.

Inequality Form:

$x > 2$

Interval Notation:

$(2, \infty)$

Solve the Inequality for x 7^(3x+4)<49^(2x+1)

Related Questions

Support LCMGCF.com by disabling your adblocker.