Question

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.

$6h-4\left(h-1\right)\le 7h-11$

Short answer

$h\ge 3$

$[3,\infty )$

Step-by-step solution

Step 1. Given information.

The following inequality is given

$6h-4\left(h-1\right)\le 7h-11$

Step 2. Solving the inequality.

Distributing and combining like terms

$$\begin{gathered} 6h-4h+4\le 7h-11 \\ 2h+4\le 7h-11 \end{gathered}$$

Subtracting $7h+4$from both sides and simplifying

$$\begin{gathered} 2h+4-\left(7h+4\right)\le 7h-11-\left(7h+4\right) \\ 2h+4-7h-4\le 7h-11-7h-4 \\ -5h\le -15 \end{gathered}$$

Dividing both sides by $-5$(this will reverse the inequality as the division is being performed by a negative quantity)

$$\begin{gathered} \frac{-5h}{5}\ge \frac{-15}{5} \\ h\ge 3 \end{gathered}$$

Step 3. Graphing the inequality on the number line. 

The graph of the solution on the number line is shown below

Step 4. Writing the solution in the interval notation.

The solution in the interval notation can be expressed as $[3,\infty )$