Question

Math

Posted 4 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 4 months ago

Solution by Steps

step 1

Combine like terms on the left side of the inequality: $4x - 3 + 6x > 5x + 7$ becomes $10x - 3 > 5x + 7$

step 2

Subtract $5x$ from both sides to isolate the variable term on one side: $10x - 5x - 3 > 7$ simplifies to $5x - 3 > 7$

step 3

Add 3 to both sides to further isolate the variable term: $5x - 3 + 3 > 7 + 3$ simplifies to $5x > 10$

step 4

Divide both sides by 5 to solve for $x$: $\frac{5x}{5} > \frac{10}{5}$ simplifies to $x > 2$

Answer

$x > 2$

Key Concept

Solving linear inequalities

Explanation

To solve a linear inequality, combine like terms, isolate the variable on one side, and then solve for the variable by performing inverse operations.

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