Questions: 2x + 5 ≤ 3x - 10

Transcript text: $2 x+5 \leq 3 x-10$

Solution

Solution Steps

To solve the inequality $2x + 5 \leq 3x - 10$, we need to isolate the variable $x$ on one side. We can do this by first subtracting $2x$ from both sides, and then adding 10 to both sides to solve for $x$.

Step 1: Rearranging the Inequality

We start with the inequality: \[ 2x + 5 \leq 3x - 10 \] To isolate $x$, we first subtract $2x$ from both sides: \[ 5 \leq x - 10 \]

Step 2: Solving for $x$

Next, we add 10 to both sides: \[ 15 \leq x \] This can be rewritten as: \[ x \geq 15 \]

Step 3: Expressing the Solution

The solution indicates that $x$ can take any value greater than or equal to 15. In interval notation, this is expressed as: \[ [15, \infty) \]

Final Answer

Thus, the solution to the inequality is: \[ \boxed{x \geq 15} \]

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