Question

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

$12x+3\left(x+7\right)>10x-24$

Short answer

$x>-9$

$(-9,\infty )$

Step-by-step solution

Step 1. Given information.

The following inequality is given:

$12x+3\left(x+7\right)>10x-24$

Step 2. Solving the inequality.

Distributing and combining like terms

$$\begin{gathered} 12x+3x+21>10x-24 \\ 15x+21>10x-24 \end{gathered}$$

Subtracting $10x+21$from both sides and simplifying

$$\begin{gathered} 15x+21-10x-21>10x-24-10x-21 \\ 5x>-45 \\ x>\frac{-45}{5} \\ x>-9 \end{gathered}$$

Step 3. Graphing the solution on the number line.

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

Step 4. Writing the solution in the interval notation.

In the interval notation, the solution can be written as

$\left(-9,\infty \right)$