Solve the Linear Inequality: 5x+8<9 Step-by-Step

Q: When do I need to flip the inequality sign?

You only flip the inequality sign when multiplying or dividing by a negative number. Since we divided by positive 5 in this problem, the sign stays the same:

Q: How can I check if my answer is correct?

Pick any number that satisfies your solution and substitute it back! For \( x , try x = 0: \( 5(0) + 8 = 8 ✓

Q: What does the solution mean on a number line?

The solution \( x means all numbers to the left of 0.2 on the number line. Use an open circle at 0.2 since it's not included.

Q: Why isn't the answer one specific number?

Inequalities have infinitely many solutions! Any value less than $ \frac{1}{5} $ works: -1, 0, 0.1, etc. This is different from equations which usually have one answer.

Q: Can I write 1/5 as a decimal instead?

Yes! $ \frac{1}{5} = 0.2 $, so you can write the answer as x . Both forms are correct, but fractions are often preferred for exact answers.

Linear Inequalities with Single Variable Solutions

Solve the following inequality:

$5x+8<9$

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Step-by-step video solution

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Step-by-step written solution

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Understand the problem

Solve the following inequality:

$5x+8<9$

Step-by-step solution

This is an inequality problem. The inequality is actually an exercise we solve in a completely normal way, except in the case that we multiply or divide by negative.

Let's start by moving the sections:

5X+8<9

5X<9-8

5X<1

We divide by 5:

X<1/5

And this is the solution!

Final Answer

$x<\frac{1}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Isolate the variable using inverse operations step-by-step
Technique: Subtract 8 from both sides: 5x < 9 - 8 = 1
Check: Test x = 0: 5(0) + 8 = 8 < 9 ✓

Common Mistakes

Avoid these frequent errors

Flipping inequality sign when dividing by positive numbers
Don't flip the < symbol when dividing 5x < 1 by positive 5 = wrong direction! The inequality sign only flips 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

When do I need to flip the inequality sign?

You only flip the inequality sign when multiplying or dividing by a negative number. Since we divided by positive 5 in this problem, the sign stays the same: < remains <.

How can I check if my answer is correct?

Pick any number that satisfies your solution and substitute it back! For $x < \frac{1}{5}$ , try x = 0: $5(0) + 8 = 8 < 9$ ✓

What does the solution mean on a number line?

The solution $x < \frac{1}{5}$ means all numbers to the left of 0.2 on the number line. Use an open circle at 0.2 since it's not included.

Why isn't the answer one specific number?

Inequalities have infinitely many solutions! Any value less than $\frac{1}{5}$ works: -1, 0, 0.1, etc. This is different from equations which usually have one answer.

Can I write 1/5 as a decimal instead?

Yes! $\frac{1}{5} = 0.2$ , so you can write the answer as x < 0.2. Both forms are correct, but fractions are often preferred for exact answers.

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