Solve for y 1/2(8y+2)+1/2(8y-4)<15

$\frac{1}{2} \cdot (8 y + 2) + \frac{1}{2} \cdot (8 y - 4) < 15$

Step 1

Simplify $\frac{1}{2} \cdot (8 y + 2) + \frac{1}{2} \cdot (8 y - 4)$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{2} (8 y) + \frac{1}{2} \cdot 2 + \frac{1}{2} \cdot (8 y - 4) < 15$

Cancel the common factor of $2$ .

Factor $2$ out of $8 y$ .

$\frac{1}{2} (2 (4 y)) + \frac{1}{2} \cdot 2 + \frac{1}{2} \cdot (8 y - 4) < 15$

Cancel the common factor.

$\frac{1}{2} (2 (4 y)) + \frac{1}{2} \cdot 2 + \frac{1}{2} \cdot (8 y - 4) < 15$

Rewrite the expression.

$4 y + \frac{1}{2} \cdot 2 + \frac{1}{2} \cdot (8 y - 4) < 15$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 y + \frac{1}{2} \cdot 2 + \frac{1}{2} \cdot (8 y - 4) < 15$

Rewrite the expression.

$4 y + 1 + \frac{1}{2} \cdot (8 y - 4) < 15$

Apply the distributive property.

$4 y + 1 + \frac{1}{2} (8 y) + \frac{1}{2} \cdot - 4 < 15$

Cancel the common factor of $2$ .

Factor $2$ out of $8 y$ .

$4 y + 1 + \frac{1}{2} (2 (4 y)) + \frac{1}{2} \cdot - 4 < 15$

Cancel the common factor.

$4 y + 1 + \frac{1}{2} (2 (4 y)) + \frac{1}{2} \cdot - 4 < 15$

Rewrite the expression.

$4 y + 1 + 4 y + \frac{1}{2} \cdot - 4 < 15$

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

$4 y + 1 + 4 y + \frac{1}{2} \cdot (2 (- 2)) < 15$

Cancel the common factor.

$4 y + 1 + 4 y + \frac{1}{2} \cdot (2 \cdot - 2) < 15$

Rewrite the expression.

$4 y + 1 + 4 y - 2 < 15$

Simplify by adding terms.

Add $4 y$ and $4 y$ .

$8 y + 1 - 2 < 15$

Subtract $2$ from $1$ .

$8 y - 1 < 15$

Step 2

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

Add $1$ to both sides of the inequality.

$8 y < 15 + 1$

Add $15$ and $1$ .

$8 y < 16$

Step 3

Divide each term in $8 y < 16$ by $8$ and simplify.

Divide each term in $8 y < 16$ by $8$ .

$\frac{8 y}{8} < \frac{16}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} < \frac{16}{8}$

Divide $y$ by $1$ .

$y < \frac{16}{8}$

Simplify the right side.

Divide $16$ by $8$ .

$y < 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y < 2$

Interval Notation:

$(- \infty, 2)$

Solve for y 1/2*(8y+2)+1/2*(8y-4)<15

Related Questions

Support LCMGCF.com by disabling your adblocker.

Solve for y 1/2(8y+2)+1/2(8y-4)<15