Solve the Inequality for t ((3-4t)-12)/2<2t+3/2

$\frac{(3 - 4 t) - 12}{2} < 2 t + \frac{3}{2}$

Step 1

Multiply both sides by $2$ .

$\frac{3 - 4 t - 12}{2} \cdot 2 < (2 t + \frac{3}{2}) \cdot 2$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{3 - 4 t - 12}{2} \cdot 2$ .

Subtract $12$ from $3$ .

$\frac{- 4 t - 9}{2} \cdot 2 < (2 t + \frac{3}{2}) \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{- 4 t - 9}{2} \cdot 2 < (2 t + \frac{3}{2}) \cdot 2$

Rewrite the expression.

$- 4 t - 9 < (2 t + \frac{3}{2}) \cdot 2$

Simplify the right side.

Simplify $(2 t + \frac{3}{2}) \cdot 2$ .

Apply the distributive property.

$- 4 t - 9 < 2 t \cdot 2 + \frac{3}{2} \cdot 2$

Multiply $2$ by $2$ .

$- 4 t - 9 < 4 t + \frac{3}{2} \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 4 t - 9 < 4 t + \frac{3}{2} \cdot 2$

Rewrite the expression.

$- 4 t - 9 < 4 t + 3$

Step 3

Solve for $t$ .

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

Subtract $4 t$ from both sides of the inequality.

$- 4 t - 9 - 4 t < 3$

Subtract $4 t$ from $- 4 t$ .

$- 8 t - 9 < 3$

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

Add $9$ to both sides of the inequality.

$- 8 t < 3 + 9$

Add $3$ and $9$ .

$- 8 t < 12$

Divide each term in $- 8 t < 12$ by $- 8$ and simplify.

Divide each term in $- 8 t < 12$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 t}{- 8} > \frac{12}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 t}{- 8} > \frac{12}{- 8}$

Divide $t$ by $1$ .

$t > \frac{12}{- 8}$

Simplify the right side.

Cancel the common factor of $12$ and $- 8$ .

Factor $4$ out of $12$ .

$t > \frac{4 (3)}{- 8}$

Cancel the common factors.

Factor $4$ out of $- 8$ .

$t > \frac{4 \cdot 3}{4 \cdot - 2}$

Cancel the common factor.

$t > \frac{4 \cdot 3}{4 \cdot - 2}$

Rewrite the expression.

$t > \frac{3}{- 2}$

Move the negative in front of the fraction.

$t > - \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$t > - \frac{3}{2}$

Interval Notation:

$(- \frac{3}{2}, \infty)$

Solve the Inequality for t ((3-4t)-12)/2<2t+3/2

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