Solve 𝑥 minus nine divided by four equals negative eight.
In order to solve this problem, we are going to use the balancing method: whatever we do to the left-hand side of the equation, we’re also gonna do to the right-hand side.
Our first step is to multiply both sides of the equation by four. Multiplying the left-hand side by four gives us 𝑥 minus nine. Multiplying the right-hand side, the negative eight, by four gives us negative 32. Our next step is to add nine to both sides of the equation. On the left-hand side, that leaves us with 𝑥 take away nine add nine and on the right-hand side negative 32 add nine.
Using the property of opposites, the nines on the left-hand side cancel, leaving us with 𝑥. And on the right-hand side, negative 32 add nine gives us negative 23. Therefore, the solution to the equation 𝑥 take away nine divided by four equals negative eight is 𝑥 equals negative 23.
We could check to see if this is the correct answer by substituting negative 23 back into our initial equation. Negative 23 take away nine gives us negative 32. When we divide this answer by four, we get negative eight. Therefore, our answer is correct.