What is the value of $x$ in the equation $\frac{1}{3} x-\frac{2}{3}=-18$?
Answer (1)
Multiply both sides of the equation by 3 to eliminate the fractions: 3 ( 3 1 x − 3 2 ) = 3 ( − 18 ) .
Simplify the equation: x − 2 = − 54 .
Add 2 to both sides of the equation to isolate x : x = − 54 + 2 .
Calculate the value of x : x = − 52 .
Explanation
Understanding the Problem We are given the equation 3 1 x − 3 2 = − 18 . Our goal is to find the value of x that satisfies this equation.
Eliminating Fractions To solve for x , we first want to eliminate the fractions. We can do this by multiplying both sides of the equation by 3: 3 × ( 3 1 x − 3 2 ) = 3 × ( − 18 ) .
Simplifying the Equation Now, we distribute the 3 on the left side of the equation: 3 × 3 1 x − 3 × 3 2 = − 54 This simplifies to: x − 2 = − 54
Isolating x Next, we want to isolate x by adding 2 to both sides of the equation: x − 2 + 2 = − 54 + 2 This gives us: x = − 52
Final Answer Therefore, the value of x that satisfies the equation is -52.
Examples
Imagine you're baking a cake and need to adjust a recipe. If the original recipe calls for 3 1 cup of sugar but you only want to make a portion that's 3 2 less sweet, you can use this equation to find out how much sugar to use. This kind of problem helps in scaling recipes or adjusting ingredient quantities based on desired outcomes, ensuring your cake turns out just right!
