Solve the Linear Inequality: 7 + 2x < 15 Step-by-Step

Q: When do I flip the inequality sign?

Only when multiplying or dividing by a negative number! In this problem, we divide by positive 2, so the inequality \( stays the same direction.

Q: How can I check if x < 4 is correct?

Pick any number less than 4 (like x = 3) and substitute: \( 7 + 2(3) = 13 ✓. Also try a number greater than 4 - it shouldn't work!

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

(doesn't include the boundary), while ≤ means "less than or equal to" (includes the boundary). Our answer x

Q: Can I graph this solution?

Yes! Draw a number line, put an open circle at 4 (since x doesn't equal 4), and shade everything to the left of 4.

Linear Inequalities with Two-Step Solutions

Solve the inequality:

$7 + 2x < 15$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the inequality:

$7 + 2x < 15$

Step-by-step solution

To solve the inequality $7 + 2x < 15$ , we start by isolating the variable $x$ .

First, subtract 7 from both sides of the inequality:

$7 + 2x - 7 < 15 - 7$

Simplifying this, we get:

$2x < 8$

Next, divide both sides by 2 to solve for $x$ :

$\frac{2x}{2} < \frac{8}{2}$

Thus, the solution is:

$x < 4$

Final Answer

$x < 4$

Key Points to Remember

Essential concepts to master this topic

Order: Subtract constants first, then divide by coefficient
Technique: 7 + 2x < 15 becomes 2x < 8, then x < 4
Check: Test x = 3: 7 + 2(3) = 13 < 15 ✓

Common Mistakes

Avoid these frequent errors

Flipping inequality sign when dividing by positive numbers
Don't flip the < sign when dividing 2x < 8 by positive 2 = wrong direction! The inequality sign only flips when multiplying or dividing by negative numbers. Always keep the same direction when dividing by 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 sign?

Only when multiplying or dividing by a negative number! In this problem, we divide by positive 2, so the inequality $<$ stays the same direction.

How can I check if x < 4 is correct?

Pick any number less than 4 (like x = 3) and substitute: $7 + 2(3) = 13 < 15$ ✓. Also try a number greater than 4 - it shouldn't work!

What's the difference between < and ≤?

< means "less than" (doesn't include the boundary), while ≤ means "less than or equal to" (includes the boundary). Our answer x < 4 means x cannot equal 4.

Can I graph this solution?

Yes! Draw a number line, put an open circle at 4 (since x doesn't equal 4), and shade everything to the left of 4.

What if I had 7 + 2x > 15 instead?

Follow the same steps: subtract 7, then divide by 2. You'd get $x > 4$ . The process is identical - only the final inequality direction changes!

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