Solve and Graph: Finding the Solution to 5-8x<7x+3

Q: How do I know which way the arrow points on the number line?

The arrow points in the direction of the inequality! Since $ x > \frac{2}{15} $, values greater than $ \frac{2}{15} $ make it true, so the arrow points right.

Q: Why is the circle open instead of filled?

An open circle means the boundary value is not included in the solution. Since we have $ x > \frac{2}{15} $ (not ≥), the point $ \frac{2}{15} $ itself doesn't satisfy the inequality.

Q: When do I flip the inequality sign?

Only when you multiply or divide both sides by a negative number. In this problem, we divided by positive 15, so the sign stays the same.

Q: What's the difference between < and ≤ on a graph?

uses an open circle (boundary not included). ≤ or ≥ uses a filled/closed circle (boundary is included). Remember: open circle = strict inequality!

Linear Inequalities with Number Line Graphs

Which diagram represents the solution to the inequality below?

$5-8x<7x+3$

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Understand the problem

Which diagram represents the solution to the inequality below?

$5-8x<7x+3$

Step-by-step solution

First, we will move the elements:

$5-8x>7x+3$

$5-3>7x+8x$
$2>15x$

We divide the answer by 13, and we get:

$x > \frac{2}{15}$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Isolate Variable: Move all terms with x to one side systematically
Combine Terms: $5-3 > 7x+8x$ becomes $2 > 15x$
Check Direction: Since we divide by positive 15, inequality direction stays same ✓

Common Mistakes

Avoid these frequent errors

Flipping inequality sign when dividing by positive numbers
Don't flip the inequality sign when dividing $2 > 15x$ by 15 = wrong direction! You only flip the sign when multiplying or dividing by negative numbers. Always keep the same direction when dividing by positive numbers.

Practice Quiz

Test your knowledge with interactive questions

Solve the inequality:

$$ 5-3x>-10 $$

FAQ

Everything you need to know about this question

How do I know which way the arrow points on the number line?

The arrow points in the direction of the inequality! Since $x > \frac{2}{15}$ , values greater than $\frac{2}{15}$ make it true, so the arrow points right.

Why is the circle open instead of filled?

An open circle means the boundary value is not included in the solution. Since we have $x > \frac{2}{15}$ (not ≥), the point $\frac{2}{15}$ itself doesn't satisfy the inequality.

When do I flip the inequality sign?

Only when you multiply or divide both sides by a negative number. In this problem, we divided by positive 15, so the sign stays the same.

How can I check if my graph is correct?

Pick a test point from the shaded region and substitute it back into the original inequality. If it makes the inequality true, your graph is correct!

What's the difference between < and ≤ on a graph?

< or > uses an open circle (boundary not included). ≤ or ≥ uses a filled/closed circle (boundary is included). Remember: open circle = strict inequality!

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