Solve the Linear Inequality: 3x+4 ≤ 10 Step-by-Step

Linear Inequalities with Integer Solutions

Solve the following inequality:

3x+410 3x+4 \leq 10

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following inequality:

3x+410 3x+4 \leq 10

2

Step-by-step solution

To solve the inequality 3x+410 3x+4 \leq 10 , follow these steps:

1. Subtract 4 from both sides: 3x6 3x \leq 6 .

2. Divide both sides by 3: x2 x \leq 2 .

3

Final Answer

x2 x \leq 2

Key Points to Remember

Essential concepts to master this topic
  • Rule: Operations preserve inequality direction except when multiplying/dividing by negatives
  • Technique: Isolate x by subtracting 4: 3x ≤ 6, then divide by 3
  • Check: Test x = 2: 3(2) + 4 = 10 ≤ 10 ✓

Common Mistakes

Avoid these frequent errors
  • Flipping inequality symbol unnecessarily
    Don't flip the inequality symbol when dividing by positive 3 = x2 x \geq 2 ! The symbol only flips when multiplying or dividing by negative numbers. Always keep the same direction when working with positive coefficients.

Practice Quiz

Test your knowledge with interactive questions

Solve the following inequality:

\( 3x+4 \leq 10 \)

FAQ

Everything you need to know about this question

When do I flip the inequality symbol?

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Only when multiplying or dividing both sides by a negative number. Since we divided by positive 3 in this problem, the symbol stays \leq .

How is this different from solving equations?

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The steps are almost identical! The key difference is that inequalities give you a range of solutions (like x ≤ 2) instead of just one number.

What does x ≤ 2 actually mean?

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It means x can be any number less than or equal to 2. So x could be 2, 1, 0, -5, -100, etc. All these values make the original inequality true!

How do I check my answer?

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Pick any number that fits your solution and substitute it back. For x2 x \leq 2 , try x = 0: 3(0)+4=410 3(0) + 4 = 4 ≤ 10

What if I get a negative coefficient for x?

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If you need to divide by a negative to isolate x, that's when you flip the inequality symbol. For example: -2x ≤ 6 becomes x ≥ -3.

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