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
[tex]\sqrt[3]{5x-4}=\sqrt[3]{7x+8}[/tex]
⇒ 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:
[tex](\sqrt[3]{5x-4})^3=(\sqrt[3]{7x+8})^3\\5x-4=7x+8[/tex]
⇒ 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:
[tex](\sqrt[3]{5x-4})^3-5x=(\sqrt[3]{7x+8})^3\\5x-4=7x+8-5x\\-4=2x+8[/tex]
⇒ Now, subtract 8 from both sides:
[tex]-4-8=2x+8-8\\-12=2x[/tex]
⇒ Finally, divide both sides by 2 to isolate x:
[tex]\dfrac{-12}{2}=\dfrac{2x}{2}\\\\-6=x[/tex]
Answer
x = -6
