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graph the solution of this inequality -2x+13<9

open circle? or closed?
left or right?

3 answers

To solve the inequality \(-2x + 13 < 9\), first isolate \(x\):

  1. Subtract 13 from both sides: \[ -2x < 9 - 13 \] \[ -2x < -4 \]

  2. Divide both sides by -2. Remember that dividing by a negative number reverses the inequality sign: \[ x > \frac{-4}{-2} \] \[ x > 2 \]

Now that we have the solution \(x > 2\), let’s graph this inequality:

  1. Open or Closed Circle: Since the inequality is strictly greater than ( \(>\) ), you would use an open circle on 2 to indicate that 2 is not included in the solution.

  2. Left or Right: The solution \(x > 2\) indicates that you shade the line to the right of 2.

Graph Representation

  • Place an open circle at \(x = 2\).
  • Shade the line to the right of the open circle to show that all values greater than 2 are included in the solution.

If you were to sketch this, it would look something like this:

---|---|---|---|---|---|---|---|-->
   0   1   2   3   4   5   6   7  

                (---)

Here, the (---) indicates shading to the right from the open circle at 2.

yay to the right from the open circle at 2. x>2

On a coordinate plane, a straight dashed line with equation y greater-than 2 x minus 4 has a positive slope and goes through (0, negative 4) and (2, 0). Everything to the left of the line is shaded.Which of the points are solutions to the inequality? Check all that apply.(–2, –5)(0, –4)(1, 1)(3, 5)(5, 5)

To determine which of the given points are solutions to the inequality represented by the dashed line with equation \(y > 2x - 4\), we will check each point by substituting the \(x\) and \(y\) coordinates into the inequality.

Inequality to test:
\[ y > 2x - 4 \]

Let's test each point:

  1. Point \((-2, -5)\): \[ -5 > 2(-2) - 4 \ -5 > -4 - 4 \ -5 > -8 \quad \text{(True)} \]

  2. Point \((0, -4)\): \[ -4 > 2(0) - 4 \ -4 > -4 \quad \text{(False; because it is not greater than)} \]

  3. Point \((1, 1)\): \[ 1 > 2(1) - 4 \ 1 > 2 - 4 \ 1 > -2 \quad \text{(True)} \]

  4. Point \((3, 5)\): \[ 5 > 2(3) - 4 \ 5 > 6 - 4 \ 5 > 2 \quad \text{(True)} \]

  5. Point \((5, 5)\): \[ 5 > 2(5) - 4 \ 5 > 10 - 4 \ 5 > 6 \quad \text{(False)} \]

Summary

The points that are solutions to the inequality \(y > 2x - 4\) are:

  • \((-2, -5)\) ✔️
  • \((1, 1)\) ✔️
  • \((3, 5)\) ✔️

The points \((0, -4)\) and \((5, 5)\) do not satisfy the inequality.

Thus, the solutions are:

  • \((-2, -5)\)
  • \((1, 1)\)
  • \((3, 5)\)