Questions: -30+4x ≤ 19x-14

Transcript text: \[ -30+4 x \leq 19 x-14 \]

Solution

Solution Steps

To solve the inequality \(-30 + 4x \leq 19x - 14\), we need to isolate the variable \(x\) on one side of the inequality. This involves moving all terms involving \(x\) to one side and constant terms to the other side, then simplifying the resulting expression.

Step 1: Rearranging the Inequality

We start with the inequality: \[ -30 + 4x \leq 19x - 14 \] Rearranging gives: \[ 4x - 19x \leq -14 + 30 \] which simplifies to: \[ -15x \leq 16 \]

Step 2: Isolating \(x\)

Next, we divide both sides by \(-15\). Remember that dividing by a negative number reverses the inequality: \[ x \geq -\frac{16}{15} \]

Step 3: Expressing the Solution

The solution can be expressed as: \[ x \geq -\frac{16}{15} \] This means \(x\) can take any value greater than or equal to \(-\frac{16}{15}\).