Solve the Inequality for x 8x^2+50x-5<10x-5

$8 x^{2} + 50 x - 5 < 10 x - 5$

Move all terms containing $x$ to the left side of the inequality.

Subtract $10 x$ from both sides of the inequality.

$8 x^{2} + 50 x - 5 - 10 x < - 5$

Subtract $10 x$ from $50 x$ .

$8 x^{2} + 40 x - 5 < - 5$

Convert the inequality to an equation.

$8 x^{2} + 40 x - 5 = - 5$

Add $5$ to both sides of the equation.

$8 x^{2} + 40 x - 5 + 5 = 0$

Combine the opposite terms in $8 x^{2} + 40 x - 5 + 5$ .

Add $- 5$ and $5$ .

$8 x^{2} + 40 x + 0 = 0$

Add $8 x^{2} + 40 x$ and $0$ .

$8 x^{2} + 40 x = 0$

Factor $8 x$ out of $8 x^{2} + 40 x$ .

Factor $8 x$ out of $8 x^{2}$ .

$8 x (x) + 40 x = 0$

Factor $8 x$ out of $40 x$ .

$8 x (x) + 8 x (5) = 0$

Factor $8 x$ out of $8 x (x) + 8 x (5)$ .

$8 x (x + 5) = 0$

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

$x = 0$

$x + 5 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

The final solution is all the values that make $8 x (x + 5) = 0$ true.

$x = 0, - 5$

Use each root to create test intervals.

$x < - 5$

$- 5 < x < 0$

$x > 0$

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.

Test a value on the interval $x < - 5$ to see if it makes the inequality true.

Choose a value on the interval $x < - 5$ and see if this value makes the original inequality true.

$x = - 8$

Replace $x$ with $- 8$ in the original inequality.

$8 {(- 8)}^{2} + 50 (- 8) - 5 < 10 (- 8) - 5$

The left side $107$ is not less than the right side $- 85$ , which means that the given statement is false.

False

Test a value on the interval $- 5 < x < 0$ to see if it makes the inequality true.

Choose a value on the interval $- 5 < x < 0$ and see if this value makes the original inequality true.

$x = - 2$

Replace $x$ with $- 2$ in the original inequality.

$8 {(- 2)}^{2} + 50 (- 2) - 5 < 10 (- 2) - 5$

The left side $- 73$ is less than the right side $- 25$ , which means that the given statement is always true.

True

Test a value on the interval $x > 0$ to see if it makes the inequality true.

Choose a value on the interval $x > 0$ and see if this value makes the original inequality true.

$x = 2$

Replace $x$ with $2$ in the original inequality.

$8 {(2)}^{2} + 50 (2) - 5 < 10 (2) - 5$

The left side $127$ is not less than the right side $15$ , which means that the given statement is false.

False

Compare the intervals to determine which ones satisfy the original inequality.

$x < - 5$ False

$- 5 < x < 0$ True

$x > 0$ False

$x < - 5$ False

$- 5 < x < 0$ True

$x > 0$ False

The solution consists of all of the true intervals.

$- 5 < x < 0$

The result can be shown in multiple forms.

Inequality Form:

$- 5 < x < 0$

Interval Notation:

$(- 5, 0)$

Solve the Inequality for x 8x^2+50x-5<10x-5

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