Question

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

$5-3x\ge 8x-7$

Short answer

The solution set of given inequality is $5-3x\ge 8x-7$that is $x\in (-\infty ,\frac{12}{11}]$.

Step-by-step solution

Step-1. Determining the solution to Inequality.

$5-3x\ge 8x-7$

$5-3x+3x\ge 8x+3x-7$ (Add 3x)

$5\ge 11x-7$ (Simplify)

$5+7\ge 11x-7+7$ (Add 7)

$12\ge 11x_{}$ (Simplify)

$\frac{12}{11}\ge \frac{11x}{11}$ (Multiply by $\frac{1}{11}$)

$x\le \frac{12}{11}$

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

The solution set consists of all numbers less than or equal to $\frac{12}{11}$. In other words, the solution to inequality is the interval$(-\infty ,\frac{12}{11}]$.

Step-3. Graphing the solution set.

$$\begin{gathered} x\le \frac{12}{11} \\ x\in (-\infty ,\frac{12}{11}] \end{gathered}$$