Question

in exercises 1 - 10, solve the inequality. graph the solution. example 1

1. 2r - 3 > 7
2. 5y + 9 ≤ 4
3. - 3 ≤ 1 - 8v
4. - 8 > - 3t - 10
5. $\frac{w}{2}+4>5$
6. $1+\frac{m}{3}leq6$
7. $\frac{p}{-8}-\frac{2}{5}>\frac{8}{5}$
8. $\frac{1}{2}+\frac{r}{-4}leq\frac{5}{6}$
9. 12.6 ≥ - 6(a + 2)
10. 14.7 ≤ 3.5(b - 4)

Explanation:

1. Solve the inequality \(-3\leq1 - 8v\):

• Step1: Isolate the variable - term

Subtract 1 from both sides of the inequality.
\(-3-1\leq1 - 8v-1\), which simplifies to \(-4\leq - 8v\).

• Step2: Solve for \(v\)

Divide both sides of the inequality by - 8. When dividing an inequality by a negative number, the direction of the inequality sign changes.
\(\frac{-4}{-8}\geq\frac{-8v}{-8}\), so \(\frac{1}{2}\geq v\), or \(v\leq\frac{1}{2}\).

1. Graph the solution:

• Draw a number - line.
• Mark a closed circle at \(\frac{1}{2}\) (because the inequality is \(\leq\), so \(\frac{1}{2}\) is included in the solution set).
• Shade the line to the left of \(\frac{1}{2}\) to represent all the values of \(v\) that satisfy the inequality.

Answer:

The solution of the inequality \(-3\leq1 - 8v\) is \(v\leq\frac{1}{2}\). The graph has a closed - circle at \(\frac{1}{2}\) and is shaded to the left.