Solving Equations
When we're solving equations, our prime goal is to isolate the variable. We can do this by using inverse operations to combine like terms.
Examples:
- The inverse operation of addition is subtraction, and vice versa.
- The inverse operation of an exponent is taking the root of the exponent, and vice versa.
Solving the Question
![\sqrt[3]{5x-4}=\sqrt[3]{7x+8}](https://img.qammunity.org/2023/formulas/mathematics/high-school/ri14azgmlgzuib43q3alldqg7udk7sxskj.png)
⇒ Here, both sides are being taken to the square root of 3. To remove this, we can raise both sides to the power of 3:
![(\sqrt[3]{5x-4})^3=(\sqrt[3]{7x+8})^3\\5x-4=7x+8](https://img.qammunity.org/2023/formulas/mathematics/high-school/fh7yedxiubsqfp79zzidpc60up5w1d8d18.png)
⇒ Let's move our x variable to the right side of the equal sign and the numbers to the left side. Start by subtracting 5x from both sides:
![(\sqrt[3]{5x-4})^3-5x=(\sqrt[3]{7x+8})^3\\5x-4=7x+8-5x\\-4=2x+8](https://img.qammunity.org/2023/formulas/mathematics/high-school/xn6uc68rvbnx1tl6p2yy90f4h398mna1ql.png)
⇒ Now, subtract 8 from both sides:

⇒ Finally, divide both sides by 2 to isolate x:

Answer
x = -6