Question

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

$4-3x\le -(1+8x)$

Short answer

The solution set of the given inequality is $x\le -1$that is $x\in (-\infty ,-1]$.

Step-by-step solution

Step-1. Determining the solution to Inequality.

$4-3x\le -(1+8x)$

$4-3x+8x\le -1-8x+8x$ (Add 8x)

$4+5x\le -1$ (Simplify)

$4-4+5x\le -1-4$ (Subtract 4)

$5x\le -5$ (Simplify)

$\frac{5x}{5}\le -\frac{5}{5}$ (Multiply by $\frac{1}{5}$)

$x\le -1$

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

The solution set consists of all numbers less than or equals to –1. In other words the solution of the inequality is in the interval$(-\infty ,-1]$

Step-3. Graphing the solution set.

$$\begin{gathered} x\le -1 \\ x\in (-\infty ,-1] \end{gathered}$$