Question

algebra 2 homework: review of inequ solve each inequality and graph its 1) -5x + 3x ≥ -10

Explanation:

Step1: Combine like terms

Combine the \(x\)-terms on the left side of the inequality \(-5x + 3x \geq -10\). So, \(-5x+3x=-2x\), and the inequality becomes \(-2x \geq -10\).

Step2: Divide by -2 (reverse inequality)

Divide both sides of the inequality \(-2x \geq -10\) by \(-2\). When dividing an inequality by a negative number, the direction of the inequality sign reverses. So we have \(\frac{-2x}{-2} \leq \frac{-10}{-2}\), which simplifies to \(x \leq 5\).

Answer:

The solution to the inequality \(-5x + 3x \geq -10\) is \(x \leq 5\). To graph this, we draw a number line, place a closed circle at \(5\) (since the inequality is "less than or equal to"), and shade the region to the left of \(5\) to represent all values of \(x\) that satisfy the inequality.