Solve for y 1/3(6y+3)+1/2(4y-8)<21

$\frac{1}{3} \cdot (6 y + 3) + \frac{1}{2} \cdot (4 y - 8) < 21$

Step 1

Simplify $\frac{1}{3} \cdot (6 y + 3) + \frac{1}{2} \cdot (4 y - 8)$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{3} (6 y) + \frac{1}{3} \cdot 3 + \frac{1}{2} \cdot (4 y - 8) < 21$

Cancel the common factor of $3$ .

Factor $3$ out of $6 y$ .

$\frac{1}{3} (3 (2 y)) + \frac{1}{3} \cdot 3 + \frac{1}{2} \cdot (4 y - 8) < 21$

Cancel the common factor.

$\frac{1}{3} (3 (2 y)) + \frac{1}{3} \cdot 3 + \frac{1}{2} \cdot (4 y - 8) < 21$

Rewrite the expression.

$2 y + \frac{1}{3} \cdot 3 + \frac{1}{2} \cdot (4 y - 8) < 21$

Cancel the common factor of $3$ .

Cancel the common factor.

$2 y + \frac{1}{3} \cdot 3 + \frac{1}{2} \cdot (4 y - 8) < 21$

Rewrite the expression.

$2 y + 1 + \frac{1}{2} \cdot (4 y - 8) < 21$

Apply the distributive property.

$2 y + 1 + \frac{1}{2} (4 y) + \frac{1}{2} \cdot - 8 < 21$

Cancel the common factor of $2$ .

Factor $2$ out of $4 y$ .

$2 y + 1 + \frac{1}{2} (2 (2 y)) + \frac{1}{2} \cdot - 8 < 21$

Cancel the common factor.

$2 y + 1 + \frac{1}{2} (2 (2 y)) + \frac{1}{2} \cdot - 8 < 21$

Rewrite the expression.

$2 y + 1 + 2 y + \frac{1}{2} \cdot - 8 < 21$

Cancel the common factor of $2$ .

Factor $2$ out of $- 8$ .

$2 y + 1 + 2 y + \frac{1}{2} \cdot (2 (- 4)) < 21$

Cancel the common factor.

$2 y + 1 + 2 y + \frac{1}{2} \cdot (2 \cdot - 4) < 21$

Rewrite the expression.

$2 y + 1 + 2 y - 4 < 21$

Simplify by adding terms.

Add $2 y$ and $2 y$ .

$4 y + 1 - 4 < 21$

Subtract $4$ from $1$ .

$4 y - 3 < 21$

Step 2

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

Add $3$ to both sides of the inequality.

$4 y < 21 + 3$

Add $21$ and $3$ .

$4 y < 24$

Step 3

Divide each term in $4 y < 24$ by $4$ and simplify.

Divide each term in $4 y < 24$ by $4$ .

$\frac{4 y}{4} < \frac{24}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} < \frac{24}{4}$

Divide $y$ by $1$ .

$y < \frac{24}{4}$

Simplify the right side.

Divide $24$ by $4$ .

$y < 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y < 6$

Interval Notation:

$(- \infty, 6)$

Solve for y 1/3*(6y+3)+1/2*(4y-8)<21

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Solve for y 1/3(6y+3)+1/2(4y-8)<21