Question

solve for f: f - 4 = 6f + 26 options: f=-5, f=5, f=-6, f=6

Explanation:

Step1: Start with the equation

We have the equation \( f - 4 = 6f + 26 \).

Step2: Subtract \( f \) from both sides

Subtracting \( f \) from both sides gives \( - 4 = 5f + 26 \).

Step3: Subtract 26 from both sides

Subtracting 26 from both sides: \( - 4 - 26 = 5f \), which simplifies to \( - 30 = 5f \).

Step4: Divide by 5

Dividing both sides by 5: \( f=\frac{-30}{5}=-6 \). Wait, no, wait, let's check again. Wait, original equation: \( f - 4 = 6f + 26 \). Let's move \( f \) to the right and 26 to the left: \( - 4 - 26 = 6f - f \), so \( - 30 = 5f \), then \( f = - 6 \)? Wait, no, wait, maybe I made a mistake. Wait, let's do it again. \( f - 4 = 6f + 26 \). Subtract \( f \) from both sides: \( - 4 = 5f + 26 \). Then subtract 26: \( - 4 - 26 = 5f \), \( - 30 = 5f \), so \( f = - 6 \)? But wait, let's check the options. Wait, the options are \( f = - 5 \), \( f = 5 \), \( f = - 6 \), \( f = 6 \). Wait, maybe I messed up. Wait, let's check the equation again. Wait, the equation is \( f - 4 = 6f + 26 \). Let's move 6f to the left and -4 to the right: \( f - 6f = 26 + 4 \), so \( - 5f = 30 \), then \( f = - 6 \). Yes, that's correct. Wait, but let's check with \( f = - 6 \): Left side: \( - 6 - 4 = - 10 \). Right side: \( 6\times(-6)+26=-36 + 26=-10 \). Yes, that works. Wait, but the first option is \( f = - 5 \), let's check \( f = - 5 \): Left: \( - 5 - 4 = - 9 \). Right: \( 6\times(-5)+26=-30 + 26=-4 \). Not equal. \( f = 5 \): Left: \( 5 - 4 = 1 \). Right: \( 30 + 26 = 56 \). No. \( f = - 6 \): Left: \( - 6 - 4 = - 10 \). Right: \( 6\times(-6)+26=-36 + 26=-10 \). Yes. Wait, but earlier when I thought \( f = - 6 \), that's correct. Wait, but let's check the steps again. So the correct answer is \( f = - 6 \).

Answer:

\( f = - 6 \) (corresponding to the option with \( f = - 6 \))