Solve 7x+ 3 is less than 5x+ 9, show the graph of the solutions on the number line❓?

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Answer

Answer

7x +3 is less than 5x + 9 7x - 5x is less than 9 - 3 2x is less than 6 x is less than 3 So, on the number line = ( - infinity,  3 )

Answer

Solving the inequality: 7x - 3 < 5x='' -='' />

We are given the inequality: 7x - 3 < 5x='' -='' 9.='' to='' solve='' this='' inequality,='' we='' need='' to='' isolate='' the='' variable='' x='' on='' one='' side='' of='' the='' inequality='' sign.='' here='' are='' the='' steps='' to='' solve='' />

1. Start by subtracting 5x from both sides of the inequality:
7x - 3 - 5x < 5x='' -='' 9='' -='' />
2x - 3 < />

2. Next, add 3 to both sides of the inequality:
2x - 3 + 3 < -9='' +='' />
2x < />

3. Divide both sides of the inequality by 2:
(2x)/2 < />
x < />

Graphing the solution on the number line:

To graph the solution x < -3='' on='' the='' number='' line,='' we='' need='' to='' represent='' all='' the='' values='' of='' x='' that='' are='' less='' than='' -3.='' here='' are='' the='' steps='' to='' graph='' />

1. Draw a horizontal number line.

2. Mark a point at -3 on the number line. You can represent it with an open circle to indicate that -3 is not included in the solution.

3. Shade the region to the left of -3. This represents all the values of x that are less than -3.

4. Add an arrow on the left side of the shaded region to indicate that the solution extends indefinitely in that direction.

The final graph will show an open circle at -3 on the number line with a shaded region to the left, and an arrow pointing to the left side.

Example of the graph:

Here is an example of how the graph would look like:

```
-∞ -6 -5 -4 -3 -2 -1 0 1 2 3
------------------------------------->
●
←
```

In this graph, the open circle represents -3, the shaded region to the left represents all the values of x that are less than -3, and the arrow indicates that the solution extends indefinitely to the left.

Conclusion:

The solution to the inequality 7x - 3 < 5x='' -='' 9='' is='' x='' />< -3.='' the='' graph='' of='' the='' solution='' on='' the='' number='' line='' shows='' all='' the='' values='' of='' x='' that='' are='' less='' than='' -3,='' represented='' by='' a='' shaded='' region='' to='' the='' left='' of='' an='' open='' circle='' at='' -3,='' with='' an='' arrow='' indicating='' the='' solution='' extends='' indefinitely='' to='' the='' left.='' -3.='' the='' graph='' of='' the='' solution='' on='' the='' number='' line='' shows='' all='' the='' values='' of='' x='' that='' are='' less='' than='' -3,='' represented='' by='' a='' shaded='' region='' to='' the='' left='' of='' an='' open='' circle='' at='' -3,='' with='' an='' arrow='' indicating='' the='' solution='' extends='' indefinitely='' to='' the='' />

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