Question

solve the inequality. graph the solution. 11. $3x - 7x + 2 < 10 - 12$

Explanation:

Step1: Simplify both sides

Combine like terms.
$$3x - 7x+2<10 - 12$$
$$-4x + 2<-2$$

Step2: Subtract 2 from both sides

$$-4x+2 - 2<-2 - 2$$
$$-4x<-4$$

Step3: Divide both sides by -4 (reverse inequality sign)

When dividing by a negative number, reverse the inequality.
$$\frac{-4x}{-4}>\frac{-4}{-4}$$
$$x > 1$$

Answer:

The solution of the inequality is \(x>1\). To graph it, draw an open circle at \(x = 1\) on the number - line (because \(x = 1\) is not included in the solution) and shade the region to the right of \(x = 1\).