Solve Linear Inequality: 6x - 2 < 4 Step-by-Step

Only when multiplying or dividing by a negative number! Since we're dividing by positive 6 in this problem, the less than sign stays the same.

Pick any number less than 1 (like x = 0) and substitute: $6(0) - 2 = -2 < 4$ ✓. If it makes the original inequality true, your solution is right!

It means all numbers to the left of 1 are solutions. Draw an open circle at 1 (since 1 is not included) and shade everything to the left.

Yes! You could divide by 6 first: $x - \frac{1}{3} < \frac{2}{3}$, then add $\frac{1}{3}$. But adding 2 first keeps the numbers simpler!

Because the inequality uses less than (<), not less than or equal to (≤). When x = 1: $6(1) - 2 = 4$, which equals 4 but doesn't make 4 < 4 true.