Precalculus Examples

${(x - 7)}^{2} (x + 3) < 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

${(x - 7)}^{2} = 0$

$x + 3 = 0$

Step 2

Set ${(x - 7)}^{2}$ equal to $0$ and solve for $x$ .

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Step 2.1

Set ${(x - 7)}^{2}$ equal to $0$ .

${(x - 7)}^{2} = 0$

Step 2.2

Solve ${(x - 7)}^{2} = 0$ for $x$ .

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Step 2.2.1

Set the $x - 7$ equal to $0$ .

$x - 7 = 0$

Step 2.2.2

Add $7$ to both sides of the equation.

$x = 7$

Step 3

Set $x + 3$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Step 3.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 4

The final solution is all the values that make ${(x - 7)}^{2} (x + 3) < 0$ true.

$x = 7, - 3$

Step 5

The solution consists of all of the true intervals.

$x < - 3$

Step 6

Convert the inequality to interval notation.

$(- \infty, - 3)$

Step 7