Question

solve each of the inequality for the variable below and graph your answer: 1. $18 + 5x \leq 50 + 9x$

Explanation:

Step1: Subtract \(5x\) from both sides

To isolate the variable terms, we subtract \(5x\) from each side of the inequality \(18 + 5x \leq 50 + 9x\). This gives us \(18 + 5x - 5x \leq 50 + 9x - 5x\), which simplifies to \(18 \leq 50 + 4x\).

Step2: Subtract 50 from both sides

Next, we subtract 50 from both sides to get the constant term on the left. So, \(18 - 50 \leq 50 + 4x - 50\), which simplifies to \(-32 \leq 4x\).

Step3: Divide by 4

Now, we divide both sides by 4 to solve for \(x\). \(\frac{-32}{4} \leq \frac{4x}{4}\), which simplifies to \(-8 \leq x\) or \(x \geq -8\).

Answer:

The solution to the inequality \(18 + 5x \leq 50 + 9x\) is \(x \geq -8\). To graph this, we draw a number line, place a closed circle at \(-8\) (since the inequality includes equality), and shade to the right of \(-8\) to represent all values of \(x\) greater than or equal to \(-8\).