Answer: To solve the equation (149)x+2=7x−3(491)x+2=7x−3, we can first express both sides with the same base.
Recall that 7=49127=4921, because 72=4972=49. Therefore, we have:
(149)x+2=(49−12)x+2=49(−12)(x+2)
(491)x+2=(492−1)x+2=49(2−1)(x+2)
Now, we can rewrite the equation as:
49−(x+2)/2=7x−3
49−(x+2)/2=7x−3
Now, both sides have the base 49. Since the bases are the same, the exponents must be equal. So:
−(x+2)/2=x−3
−(x+2)/2=x−3
Now, let's solve for xx:
−(x+2)/2=x−3
−(x+2)/2=x−3
Multiply both sides by 2 to get rid of the fraction:
−x−2=2(x−3)
−x−2=2(x−3)
−x−2=2x−6
−x−2=2x−6
Add xx to both sides:
−2=3x−6
−2=3x−6
Add 6 to both sides:
4=3x
4=3x
Divide both sides by 3:
x=43
x=34
So, the solution to the equation is x=4/3. :)
