Question

1. solve the inequality, write the solution in set notation, and graph the solution set. -2(3x - 1) < 8 solution set: ______________ graph:

Explanation:

Step1: Expand the left - hand side

First, expand $-2(3x - 1)$ using the distributive property $a(b - c)=ab - ac$. Here, $a=-2$, $b = 3x$, and $c = 1$. So, $-2(3x - 1)=-6x+2$. The inequality becomes $-6x + 2<8$.

Step2: Isolate the variable term

Subtract 2 from both sides of the inequality: $-6x+2 - 2<8 - 2$. This simplifies to $-6x<6$.

Step3: Solve for x

Divide both sides of the inequality by - 6. When dividing an inequality by a negative number, the direction of the inequality sign changes. So, $\frac{-6x}{-6}>\frac{6}{-6}$, which gives $x>-1$.

Step4: Write the solution in set - notation

The solution in set - notation is $\{x|x > - 1\}$.

Step5: Graph the solution set

On a number line, draw an open circle at - 1 (because $x$ is strictly greater than - 1, not equal to it) and shade the line to the right of - 1.

Answer:

Solution Set: $\{x|x > - 1\}$
Graph: Draw an open circle at - 1 on the number line and shade to the right.