Solve the Linear Inequality: 10x-4 ≤ -3x-8
Linear Inequalities with Variable Terms
What is the solution to the following inequality?
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Understand the problem
What is the solution to the following inequality?
Step-by-step solution
In the exercise, we have an inequality equation.
We treat the inequality as an equation with the sign -=,
And we only refer to it if we need to multiply or divide by 0.
We start by organizing the sections:
Divide by 13 to isolate the X
Let's look again at the options we were asked about:
Answer A is with different data and therefore was rejected.
Answer C shows a case where X is greater than, although we know it is small, so it is rejected.
Answer D shows a case (according to the white circle) where X is not equal to, and only smaller than it. We know it must be large and equal, so this answer is rejected.
Therefore, answer B is the correct one!
Final Answer
Key Points to Remember
- Rule: Collect like terms on opposite sides of inequality
- Technique: Add 3x to both sides: 13x - 4 ≤ -8
- Check: Test x = -1: 10(-1) - 4 = -14, -3(-1) - 8 = -5, -14 ≤ -5 ✓
Common Mistakes
- Flipping inequality sign when dividing by positive number Don't flip the ≤ sign when dividing 13x ≤ -4 by positive 13 = wrong direction! The inequality sign only flips when multiplying or dividing by a negative number. Always keep the same direction when dividing by positive numbers.
Practice Quiz
Solve the inequality:
\( 5-3x>-10 \)
FAQ
When do I flip the inequality sign?
+Only when multiplying or dividing by a negative number! If you multiply or divide both sides by a positive number, the inequality direction stays the same.
How do I graph x ≤ -4/13 on a number line?
+Draw a filled circle at (because of ≤) and shade to the left since x is less than or equal to that value.
What's the difference between < and ≤?
+≤ means 'less than or equal to' so you include the boundary point (filled circle). < means 'less than' so you exclude it (open circle).
Can I move terms to either side?
+Yes! You can move to the right or to the left. The key is to keep like terms together and maintain the inequality balance.
How do I check if my solution is correct?
+Pick any number that satisfies your solution and substitute it into the original inequality. For example, try x = -1: does ? Yes, ✓
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