Solve the Inequality for y 8(6-y)<24.2-7y

$8 (6 - y) < 24.2 - 7 y$

Step 1

Simplify $8 (6 - y)$ .

Rewrite.

$0 + 0 + 8 (6 - y) < 24.2 - 7 y$

Simplify by adding zeros.

$8 (6 - y) < 24.2 - 7 y$

Apply the distributive property.

$8 \cdot 6 + 8 (- y) < 24.2 - 7 y$

Multiply.

Multiply $8$ by $6$ .

$48 + 8 (- y) < 24.2 - 7 y$

Multiply $- 1$ by $8$ .

$48 - 8 y < 24.2 - 7 y$

Step 2

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

Add $7 y$ to both sides of the inequality.

$48 - 8 y + 7 y < 24.2$

Add $- 8 y$ and $7 y$ .

$48 - y < 24.2$

Step 3

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

Subtract $48$ from both sides of the inequality.

$- y < 24.2 - 48$

Subtract $48$ from $24.2$ .

$- y < - 23.8$

Step 4

Divide each term in $- y < - 23.8$ by $- 1$ and simplify.

Divide each term in $- y < - 23.8$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{- 23.8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{- 23.8}{- 1}$

Divide $y$ by $1$ .

$y > \frac{- 23.8}{- 1}$

Simplify the right side.

Divide $- 23.8$ by $- 1$ .

$y > 23.8$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$y > 23.8$

Interval Notation:

$(23.8, \infty)$

Solve the Inequality for y 8(6-y)<24.2-7y

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