Solve for x 1/2x+3/2(x+1)-1/4=5 ?

$\frac{1}{2} x + \frac{3}{2} (x + 1) - \frac{1}{4} = 5$ ?

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

Simplify each term.

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} + \frac{3}{2} \cdot (x + 1) - \frac{1}{4} = 5$

Apply the distributive property.

$\frac{x}{2} + \frac{3}{2} x + \frac{3}{2} \cdot 1 - \frac{1}{4} = 5$

Combine $\frac{3}{2}$ and $x$ .

$\frac{x}{2} + \frac{3 x}{2} + \frac{3}{2} \cdot 1 - \frac{1}{4} = 5$

Multiply $\frac{3}{2}$ by $1$ .

$\frac{x}{2} + \frac{3 x}{2} + \frac{3}{2} - \frac{1}{4} = 5$

Simplify terms.

Combine the numerators over the common denominator.

$\frac{x + 3 x + 3}{2} + \frac{- 1}{4} = 5$

Add $x$ and $3 x$ .

$\frac{4 x + 3}{2} + \frac{- 1}{4} = 5$

Move the negative in front of the fraction.

$\frac{4 x + 3}{2} - \frac{1}{4} = 5$

To write $\frac{4 x + 3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x + 3}{2} \cdot \frac{2}{2} - \frac{1}{4} = 5$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 x + 3}{2}$ by $\frac{2}{2}$ .

$\frac{(4 x + 3) \cdot 2}{2 \cdot 2} - \frac{1}{4} = 5$

Multiply $2$ by $2$ .

$\frac{(4 x + 3) \cdot 2}{4} - \frac{1}{4} = 5$

Combine the numerators over the common denominator.

$\frac{(4 x + 3) \cdot 2 - 1}{4} = 5$

Simplify the numerator.

Apply the distributive property.

$\frac{4 x \cdot 2 + 3 \cdot 2 - 1}{4} = 5$

Multiply $2$ by $4$ .

$\frac{8 x + 3 \cdot 2 - 1}{4} = 5$

Multiply $3$ by $2$ .

$\frac{8 x + 6 - 1}{4} = 5$

Subtract $1$ from $6$ .

$\frac{8 x + 5}{4} = 5$

Multiply both sides by $4$ .

$\frac{8 x + 5}{4} \cdot 4 = 5 \cdot 4$

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{8 x + 5}{4} \cdot 4 = 5 \cdot 4$

Rewrite the expression.

$8 x + 5 = 5 \cdot 4$

Simplify the right side.

Multiply $5$ by $4$ .

$8 x + 5 = 20$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$8 x = 20 - 5$

Subtract $5$ from $20$ .

$8 x = 15$

Divide each term in $8 x = 15$ by $8$ and simplify.

Divide each term in $8 x = 15$ by $8$ .

$\frac{8 x}{8} = \frac{15}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{15}{8}$

Divide $x$ by $1$ .

$x = \frac{15}{8}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15}{8}$

Decimal Form:

$x = 1.875$

Mixed Number Form:

$x = 1 \frac{7}{8}$

Solve for x 1/2x+3/2(x+1)-1/4=5 ?

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