Solve the Linear Inequality: 5-3x>-10 Step-by-Step

Linear Inequalities with Sign Reversal

Solve the inequality:


53x>10 5-3x>-10

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1

Understand the problem

Solve the inequality:


53x>10 5-3x>-10

2

Step-by-step solution

Inequality equations will be solved like a regular equation, except for one rule:

If we multiply the entire equation by a negative, we will reverse the inequality sign.

We start by moving the sections, so that one side has the variables and the other does not:

-3x>-10-5

-3x>-15

Divide by 3

-x>-5

Divide by negative 1 (to get rid of the negative) and remember to reverse the sign of the equation.

x<5

3

Final Answer

5>x 5 > x

Key Points to Remember

Essential concepts to master this topic
  • Rule: Reverse inequality sign when dividing or multiplying by negative
  • Technique: Divide -3x > -15 by -3 to get x < 5
  • Check: Test x = 3: 5 - 3(3) = -4 > -10 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to reverse inequality sign when dividing by negative
    Don't divide -3x > -15 by -3 and keep > sign = x > 5! This gives completely opposite answer. Always reverse the inequality sign whenever you multiply or divide both sides by a negative number.

Practice Quiz

Test your knowledge with interactive questions

Solve the inequality:


\( 5-3x>-10 \)

FAQ

Everything you need to know about this question

Why do we reverse the inequality sign when dividing by negative?

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Think of it this way: 6<2 -6 < -2 is true, but when we divide by -1, we get 6>2 6 > 2 . The relationship flips because negatives reverse the order on a number line!

How do I know when to reverse the sign?

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Only reverse when you multiply or divide both sides by a negative number. Adding or subtracting negatives doesn't change the inequality direction.

What does x < 5 mean in real terms?

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It means any number less than 5 will make the original inequality true. Try x = 0: 53(0)=5>10 5 - 3(0) = 5 > -10

Can I check my answer by plugging in numbers?

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Yes! Pick any number less than 5 (like x = 2) and substitute: 53(2)=1>10 5 - 3(2) = -1 > -10 . If it's true, your solution is correct!

What if I get confused about which way the inequality should go?

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Write down the rule: "Divide or multiply by negative = flip the sign". Then double-check by testing a simple number in your final answer.

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