Inequalities

With Scientific Notebook you can solve inequalities directly.

$\blacktriangleright$ To solve an inequality

1.
Leave the insertion point in the inequality.

2.
From the Solve submenu, choose Exact.

$\blacktriangleright$ Solve + Exact

16 - 7y≥10y - 4, Solution is : y${\frac{{20}}{{17}}}$


x3 +1 > x2 + x, Solution is : $\left\{\vphantom{ -1<x,x\neq 1}\right.$ -1 < x, x≠1$\left.\vphantom{ -1<x,x\neq 1}\right\}$


$\left\vert\vphantom{ 2x+3}\right.$2x + 3$\left.\vphantom{ 2x+3}\right\vert$≤1, Solution is : $\left\{\vphantom{ -2\leq x,x\leq
-1}\right.$ -2≤x, x≤ - 1$\left.\vphantom{ -2\leq x,x\leq
-1}\right\}$


${\dfrac{{7-2x}}{{x-2}}}$≥ 0, Solution is : {2≤x, x${\frac{{7}}{{2}%
}}$}


x2 +2x - 3 > 0, Solution is : $\left\{\vphantom{ x<-3}\right.$x < - 3$\left.\vphantom{ x<-3}\right\}$$\left\{\vphantom{ 1<x}\right.$1 < x$\left.\vphantom{ 1<x}\right\}$


Note the different format of this last response. When a list of inequalities is enclosed in a single pair of braces and separated by commas, such as $\left\{\vphantom{ -1<x,\;x\neq 1}\right.$ -1 < x,  x≠1$\left.\vphantom{ -1<x,\;x\neq 1}\right\}$, all the inequalities must hold for x to be a solution. However, when the inequalities are enclosed in separate braces, such as $\left\{\vphantom{ x<-3}\right.$x < - 3$\left.\vphantom{ x<-3}\right\}$$\left\{\vphantom{ 1<x}\right.$1 < x$\left.\vphantom{ 1<x}\right\}$, any point that satisfies any of the inequalities is a solution.

The solution to this last inequality can also be read from the graph of the polynomial y = x2 + 2x - 3. In the next plot, you see that the graph passes through the x-axis at x = - 3 and x = 1, and the solution includes every point to the left of -3 or to the right of 1.

$\blacktriangleright$ Plot 2D + Rectangular

x2 + 2x - 3

dtbpF2.7717in1.8472in0ptFigure