Unit Name: Polynomial and Rational Functions

Solve the following inequality algebraically. Explain your process.

$8x-3\le 2x+1\le 17x-8$

Solve the following inequality algebraically. Explain your process.

Juan Hewlett
2021-12-11
Answered

Unit Name: Polynomial and Rational Functions

Solve the following inequality algebraically. Explain your process.

$8x-3\le 2x+1\le 17x-8$

Solve the following inequality algebraically. Explain your process.

You can still ask an expert for help

Karen Robbins

Answered 2021-12-12
Author has **49** answers

Split the inequality into two:

$8x-3\le 2x+1\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}2x+1\le 17x-8$

Isolate x from each inequality using inverse operations.

$8x-3\le 2x+1$

$8x-2x\le 3+1$

$6x\le 4$

$x\le \frac{2}{3}$

AND

$2x+1\le 17x-8$

$2x-17x\le -8-1$

$-15x+15x\le -9+15x$

$0\le -9+15x$

$\frac{3}{5}\le x$

Therefore, the solution is:$\frac{3}{5}\le x\le \frac{2}{3}$

Isolate x from each inequality using inverse operations.

AND

Therefore, the solution is:

Shannon Hodgkinson

Answered 2021-12-13
Author has **34** answers

Solve the following inequality algebraically.

Explain your process.

$8x-3\le 2x+1\le 17x-8$

We've$8x-3\le 2x+1\le 17x-8$ . (1)

$\Rightarrow 8x-3-1\le 2x+1-1\le 17x-8-1$

$\Rightarrow 8x-4\le 2x\le 17x-9$

Now dividing above equation by 2 we get

$\Rightarrow \frac{8x-4}{2}\le \frac{2x}{2}\le \frac{17}{2}x-\frac{9}{2}$

$\Rightarrow 4x-2\le x\le \frac{17}{2}x-\frac{9}{2}$ (2)

Now from equation (2) we've two cases.

(1)$x\ge 4x-2$

$\Rightarrow$ adding 2 to both sides we get

$\Rightarrow x+2\ge 4x-2+2$

$\Rightarrow x+2\ge 4x$

Subtracting x from both sides

$\Rightarrow x+2-x\ge 4x-x$

$\Rightarrow 2\ge 3x$

$\Rightarrow x\le \frac{2}{3}$

$x\le \frac{17}{2}x-\frac{9}{2}$

adding$\frac{9}{2}$ to both sides we get

$\Rightarrow x+\frac{9}{2}\le \frac{17}{2}x-\frac{9}{2}+\frac{9}{2}$

$\Rightarrow x+\frac{9}{2}\le \frac{17}{2}x$

Subtracting x from both sides

$\Rightarrow x+\frac{9}{2}-x\le \frac{17}{2}x-x$

$\Rightarrow \frac{q}{2}\le \frac{17x-2x}{2}$

$\Rightarrow \frac{9}{2}\le \frac{15x}{2}$

Multiplying 2 to both sides we get

$\text{Undefined control sequence cancel}$

$\Rightarrow 9\le 15x$

$\Rightarrow x\ge \frac{3}{5}$ (4)

From equation (3) and equation (4) we get

$\frac{3}{5}\le x\le \frac{2}{3}$

$\Rightarrow 0.6\le x\le 0.6666$

Explain your process.

We've

Now dividing above equation by 2 we get

Now from equation (2) we've two cases.

(1)

Subtracting x from both sides

adding

Subtracting x from both sides

Multiplying 2 to both sides we get

From equation (3) and equation (4) we get

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