Question

Solve the inequality. $$ 4 x-1>7 \text { or } 5 x-1<-6 $$

Short answer

The solution to the inequality is \(x > 2\) or \(x < -1\).

Step-by-step solution

Solving the first inequality: \(4x - 1 > 7\)

Starting with the first inequality, \(4x - 1 > 7\), we isolate x by first adding 1 to both sides of the inequality which results in \(4x > 8\). Then, we divide both sides of the inequality by 4 which gives us \(x > 2\).

Solving the second inequality: \(5x - 1 < -6\)

Similarly, we start solving the second inequality, \(5x - 1 < -6\), again by adding 1 to both sides of the inequality, resulting in \(5x < -5\). Then, we divide both sides of the inequality by 5, which gives us \(x < -1\).

Union of solutions

Since the inequalities are connected by the operator 'or', the solution is the union of the solutions of the two inequalities. Therefore, x can be any value greater than 2 or any value less than -1.