Question

solve the inequality and graph the solution.
2(k + 3) - 8 > 6
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
← -5 -4 -3 -2 -1 0 1 2 3 4 5 →

Explanation:

Step1: Simplify the left - hand side

First, expand $2(k + 3)$ using the distributive property $a(b + c)=ab+ac$. Here $a = 2$, $b=k$, $c = 3$, so $2(k + 3)=2k+6$. Then the inequality becomes $2k+6 - 8>6$. Combine like terms: $2k - 2>6$.

Step2: Isolate the variable term

Add 2 to both sides of the inequality. Using the addition property of inequalities, if $a>b$, then $a + c>b + c$. So $2k-2 + 2>6 + 2$, which simplifies to $2k>8$.

Step3: Solve for k

Divide both sides of the inequality by 2. Using the division property of inequalities, if $a>b$ and $c>0$, then $\frac{a}{c}>\frac{b}{c}$. So $\frac{2k}{2}>\frac{8}{2}$, which gives $k > 4$.

Answer:

The solution of the inequality is $k>4$. On the number - line, we have an open circle at 4 (since 4 is not included in the solution set) and an arrow pointing to the right.