Question

an inequality is shown. -3x + 5 < 2(x - 10) solve the inequality and graph the solution on the number line.

Explanation:

Step1: Expand the right - hand side

Expand $2(x - 10)$ using the distributive property $a(b - c)=ab - ac$. So $2(x - 10)=2x-20$. The inequality becomes $-3x + 5<2x-20$.

Step2: Move x - terms to one side

Add $3x$ to both sides of the inequality: $-3x+3x + 5<2x+3x-20$, which simplifies to $5 < 5x-20$.

Step3: Move constant terms to the other side

Add 20 to both sides: $5 + 20<5x-20 + 20$, resulting in $25<5x$.

Step4: Solve for x

Divide both sides by 5: $\frac{25}{5}<\frac{5x}{5}$, so $5 < x$ or $x>5$.

To graph $x > 5$ on the number line:

1. Draw an open circle at $x = 5$ (because $x$ is strictly greater than 5, not equal to 5).
2. Draw an arrow to the right of 5 to represent all the values of $x$ that are greater than 5.

Answer:

The solution of the inequality is $x>5$. On the number - line, there is an open circle at 5 and an arrow pointing to the right.