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Aleks [24]
4 years ago
10

Which system of inequalities is represented on this graph?

Mathematics
2 answers:
Alenkasestr [34]4 years ago
5 0

Answer:

It is the second answer choice

Step-by-step explanation:


Paul [167]4 years ago
3 0

Answer:

The correct option is 2.

Step-by-step explanation:

If a line passes through two points (x_1,y_1) and (x_2,y_2), then the equation of line is

y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)

From the given graph it is clear that the solid line passes through the points (0,2) and (1,0). So, the related equation of solid line is

y-2=\frac{0-2}{1-0}(x-0)

y-2=-2x

Add 2 on both sides.

y=-2x+2

The sign of inequality must be ≤ because the points on the line are included in the solution set and the shaded region is below the line.

y\leq -2x+2                 .... (1)

From the given graph it is clear that the solid line passes through the points (0,-1) and (1,0). So, the related equation of solid line is

y-(-1)=\frac{0-(-1)}{1-0}(x-0)

y+1=x

Subtract 1 from both sides.

y=x-1

The sign of inequality must be < because the points on the line are not included in the solution set and the shaded region is below the line.

y                 .... (2)

The system of inequalities is

y\leq -2x+2

y

Therefore, the correct option is 2.

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1x -8 &lt; 2x + 1<br> What is the largest integer value that makes this inequality true
professor190 [17]

Answer:

The largest integer value that makes the inequality true is 9.

General Formulas and Concepts:
<u>Algebra I</u>

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

Terms/Coefficients

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify.</em>

1x - 8 < 2x + 1

<u>Step 2: Solve for </u><u><em>x</em></u>

  1. Simplify:                                                                                                            x - 8 < 2x + 1
  2. [Subtraction Property of Equality] Subtract <em>x</em> on both sides:                        -8 < x + 1
  3. [Subtraction Property of Equality] Subtract 1 on both sides:                        -8 < x
  4. Rewrite:                                                                                                           x > -8

∴ we see that any number <em>x greater than -8</em> would work as a solution to the inequality. That would mean the next largest integer, 9, would be our answer.

---

Topic: Algebra I

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Step-by-step explanation:

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Step-by-step explanation:

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