Question

Solve the equation and inequality graphically.

(a)$x^3-9x-1=0$

(b)$x^2-1\le |x+1|$

Short answer

1. The solution of equation is $-2.943,0.111,\mathrm{and}3.054$.
2. The solution of inequality is $(-1,2)$.

Step-by-step solution

Part a. Step 1. Determining the abscissa a and ordinate.

Here, the abscissa is x-axis and ordinate isy-axis

Part a. Step 2. Plotting the graph.

Part a. Step 3. solution of the equation.

The three x-intercept gives the three solutions.

$x\propto -2.943,x\propto -0.111\mathrm{and}x\propto 3.054$

Part b. Step 1. Determining the equation of graph.

$$\begin{gathered} x^2-1\le |x+1| \\ \mathrm{let}{y}_1=x^2-1\mathrm{and}{y}_2=1x+11 \\ \therefore y_1\le y_2 \end{gathered}$$

Part b. Step 2. Plot the graph of y1.

$y_1=x^2-1$

Part b. Step 3. Plot the graph of y2 with y1.

$y_2=1x+11$

Solution of inequality

Since, $y_1\le y_2$

To determine the appropriate interval, we look for the x-coordinate of points where the graph intersect. We conclude that the solution is (approximately) the interval $(-1,2)$.