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Chapter 6: Problem 23

Solve the inequality. $$-5 \leq 6 x-12$$

Short Answer

Expert verified
The solution to the inequality is \(x \geq 7/6\).

Step by step solution

01

Add the constant to both sides

Start by adding 12 to both sides of the inequality in order to eliminate the constant from the side of the variable: \(-5 + 12 \leq 6x - 12 + 12\) This simplifies to: \(7 \leq 6x\).
02

Divide by the coefficient of x

Next, divide both sides of the inequality by 6 to isolate \(x\). Recall that dividing both sides of an inequality does not change the direction of the inequality symbol unless one is dividing by a negative number, which is not the case here: \(7/6 \leq x\). Therefore, the solution to the inequality \(-5 \leq 6x - 12\) is \(x \geq 7/6\).

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