Question

what value is a member of solution set for this inequality? 2x + 6 > -2
o -10
o -7
o -4
o 2
which graph represents the solution set of 2x - 5 < 3?

Explanation:

Step1: Solve the first inequality

Subtract 6 from both sides of $2x + 6> - 2$.
$2x+6 - 6>-2 - 6$, which simplifies to $2x>-8$.

Step2: Isolate x

Divide both sides of $2x>-8$ by 2.
$\frac{2x}{2}>\frac{-8}{2}$, so $x > - 4$.

Among the options -10, -7, -4, 2, the value 2 is a member of the solution - set since $2>-4$.

Step3: Solve the second inequality

Add 5 to both sides of $2x - 5<3$.
$2x-5 + 5<3 + 5$, which simplifies to $2x<8$.

Step4: Isolate x

Divide both sides of $2x<8$ by 2.
$\frac{2x}{2}<\frac{8}{2}$, so $x < 4$.
The graph of $x < 4$ has an open - circle at 4 and an arrow pointing to the left.

Answer:

For the first question: 2
For the second question: The graph with an open - circle at 4 and an arrow pointing to the left.