Question

(1/49)^x<(1/7)^x+3

Answer 1

Ответ на прилагаемом файле

Answer 2

To solve the inequality (1/49)^x < (1/7)^(x+3), we can simplify the expression and then manipulate it algebraically. Let's begin:

First, we need to simplify both sides of the inequality. Using the properties of exponents, we have:

(1/49)^x < (1/7)^(x+3) (7^(-2))^x < (7^(-1))^(x+3) 7^(-2x) < 7^(-x-3)

Since the bases are the same (7), we can equate the exponents:

-2x < -x - 3

Next, we'll solve for x by isolating the variable on one side of the inequality. Let's add 2x to both sides:

-2x + 2x < -x + 2x - 3 0 < -x - 3

To get rid of the negative sign, we can multiply both sides by -1. Remember that when you multiply or divide an inequality by a negative number, the inequality sign flips.

0 * (-1) > (-x - 3) * (-1) 0 > x + 3

Finally, subtract 3 from both sides:

0 - 3 > x + 3 - 3 -3 > x

Therefore, the solution to the inequality (1/49)^x < (1/7)^(x+3) is x < -3.