Solve the Inequality for p 8p-2>=10p-3

$8 p - 2 \geq 10 p - 3$

Step 1

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

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

$8 p - 2 - 10 p \geq - 3$

Subtract $10 p$ from $8 p$ .

$- 2 p - 2 \geq - 3$

Step 2

Move all terms not containing $p$ to the right side of the inequality.

Add $2$ to both sides of the inequality.

$- 2 p \geq - 3 + 2$

Add $- 3$ and $2$ .

$- 2 p \geq - 1$

Step 3

Divide each term in $- 2 p \geq - 1$ by $- 2$ and simplify.

Divide each term in $- 2 p \geq - 1$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 p}{- 2} \leq \frac{- 1}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 p}{- 2} \leq \frac{- 1}{- 2}$

Divide $p$ by $1$ .

$p \leq \frac{- 1}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$p \leq \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$p \leq \frac{1}{2}$

Interval Notation:

$(- \infty, \frac{1}{2}]$

Solve the Inequality for p 8p-2>=10p-3

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