Question

Math

Posted 5 months ago

```
What is the solution set for the following inequality?
$4 x-3+6 x>5 x+7$
```

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Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

Combine like terms on the left side of the inequality: $4x - 3 + 6x > 5x + 7$

step 2

Simplify the left side: $10x - 3 > 5x + 7$

step 3

Subtract $5x$ from both sides: $10x - 5x - 3 > 7$

step 4

Simplify: $5x - 3 > 7$

step 5

Add 3 to both sides: $5x - 3 + 3 > 7 + 3$

step 6

Simplify: $5x > 10$

step 7

Divide both sides by 5: $x > \frac{10}{5}$

step 8

Simplify: $x > 2$

Answer

The solution set is $x > 2$

Key Concept

Solving linear inequalities

Explanation

To solve a linear inequality, combine like terms, isolate the variable on one side, and perform inverse operations to simplify.

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