Choose the correct solution graph for the inequality.

Question

Choose the correct solution graph for the inequality.

7x+2≥30 or 2x-3≤-11

Answer 1

The correct solution graph is:

\begin{tikzpicture}
\draw[->] (-2,0) -- (4,0) node[right] {$x$};
\draw[->] (0,-2) -- (0,4) node[above] {$y$};
\draw[thick, color=blue] (-2,3) -- (2,-1);
\draw[thick, color=blue] (2,-1) -- (4,3);
\end{tikzpicture}

Answer 2

Don't understand how the robot could answer this question, since

no graph could have been shown.

Answer 3

To find the solution graph for the given inequality, let's solve each inequality separately and then graph the solutions.

First, let's solve the inequality 7x+2≥30:
Subtract 2 from both sides:
7x ≥ 30 - 2
7x ≥ 28
Divide both sides by 7 (since the coefficient of x is 7):
x ≥ 4

Next, let's solve the inequality 2x-3≤-11:
Add 3 to both sides:
2x ≤ -11 + 3
2x ≤ -8
Divide both sides by 2 (since the coefficient of x is 2):
x ≤ -4

Now, let's graph the solutions on a number line:
On the number line, draw a closed circle at x = 4 (since x ≥ 4) and shade to the right.
On the number line, draw a closed circle at x = -4 (since x ≤ -4) and shade to the left.

The correct solution graph for the given inequality is:

<-----------[●-------------->

Answer 4

To find the solution graph for the inequality 7x + 2 ≥ 30 or 2x - 3 ≤ -11, we need to solve each inequality separately and then combine the solution graphs.

Let's start with the first inequality:
7x + 2 ≥ 30

Subtracting 2 from both sides:
7x ≥ 28

Dividing both sides by 7, we get:
x ≥ 4

So the solution for the first inequality is x ≥ 4.

Now let's move on to the second inequality:
2x - 3 ≤ -11

Adding 3 to both sides:
2x ≤ -8

Dividing both sides by 2:
x ≤ -4

So the solution for the second inequality is x ≤ -4.

To represent these solutions graphically, we need to draw number lines and shade the regions that satisfy each inequality.

For the first inequality, x ≥ 4, we shade the region to the right of 4 on the number line, including 4:

<-----------[x ≥ 4]--------------------------------------------->

For the second inequality, x ≤ -4, we shade the region to the left of -4 on the number line, including -4:

<-----------[x ≤ -4]--------------------------------------------->

Now we need to find the overlapping region between these two solutions. Since there is no overlap in this case, the solution graph is empty.

Therefore, there is no correct solution graph for the given inequality since the two solutions do not overlap.