Questions: Solve the inequality and write your answer in interval notation. 13x + 10 < -20 + 4x

Transcript text: Solve the inequality and write your answer in interval notation. \[ 13 x+10<-20+4 x \]

Solution

Step 1: Rearranging the Inequality

We start with the inequality: \[ 13x + 10 < -20 + 4x \] Rearranging gives us: \[ 13x - 4x < -20 - 10 \] which simplifies to: \[ 9x < -30 \]

Step 2: Isolating \(x\)

Next, we isolate \(x\) by dividing both sides by 9: \[ x < -\frac{30}{9} \] This simplifies to: \[ x < -\frac{10}{3} \]

Step 3: Writing in Interval Notation

The solution in interval notation is: \[ (-\infty, -\frac{10}{3}) \]

\(\boxed{(-\infty, -\frac{10}{3})}\)

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