Question

Solve the linear Inequality. Express the solution using interval notation and graph the solution set.

$2(7x-3)\le 12x+16$

Short answer

The solution set of the given inequality is $x\le \frac{21}{2}$that is $x\in (-\infty ,\frac{21}{2}]$.

Step-by-step solution

Step-1. Determining the solution to Inequality.

$2(7x-3)\le 12x+16$

$14x-6\le 12x+16$ (Simplify)

$14x-12x-6\le 12x-12x+16$ (Subtract)

$2x-6\le 16$ (Simplify)

$2x-6+6\le 16+6$ (Add)

$2x\le 21$ (Simplify)

$\frac{2x}{2}\le \frac{21}{2}$ (Multiply by $\frac{1}{2}$)

$x\le \frac{21}{2}$

Step-2. Expressing the solution set in Interval Notation.

The solution set consists of all numbers less than or equals to $\frac{21}{2}$. In other words the solution of the inequality is in the interval$(-\infty ,\frac{21}{2}]$.

Step-3. Graphing the solution set.

$$\begin{gathered} x\le \frac{21}{2} \\ x\in (-\infty ,\frac{21}{2}] \end{gathered}$$