Solve the Linear Inequality: 6x+d < 3x+1 Step by Step

You only flip the inequality sign when multiplying or dividing by a negative number. Since 3 is positive, the inequality direction stays the same: $x < \frac{1-d}{3}$.

The parameter d is a constant value that affects where the boundary line is located. Different values of d will shift the solution region, but the inequality structure remains the same.

Rewrite $x < \frac{1-d}{3}$ by distributing the division: $x < \frac{1}{3} - \frac{d}{3}$, which equals $x < -\frac{1}{3}d + \frac{1}{3}$.

Yes! You could subtract d from both sides first to get $6x < 3x + 1 - d$, then subtract 3x. Both approaches give the same final answer.

No, the solving process stays exactly the same! Whether d is positive, negative, or zero, you follow the same steps. The value of d only affects the numerical boundary, not the inequality direction.