Solve the Inequality for x -5+3/4(5x-1)<1

$- 5 + \frac{3}{4} (5 x - 1) < 1$

Simplify $- 5 + \frac{3}{4} \cdot (5 x - 1)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $\frac{3}{4} (5 x)$ .

Combine $5$ and $\frac{3}{4}$ .

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

Multiply $5$ by $3$ .

$- 5 + \frac{15}{4} x + \frac{3}{4} \cdot - 1 < 1$

Combine $\frac{15}{4}$ and $x$ .

$- 5 + \frac{15 x}{4} + \frac{3}{4} \cdot - 1 < 1$

Multiply $\frac{3}{4} \cdot - 1$ .

Combine $\frac{3}{4}$ and $- 1$ .

$- 5 + \frac{15 x}{4} + \frac{3 \cdot - 1}{4} < 1$

Multiply $3$ by $- 1$ .

$- 5 + \frac{15 x}{4} + \frac{- 3}{4} < 1$

Move the negative in front of the fraction.

$- 5 + \frac{15 x}{4} - \frac{3}{4} < 1$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{15 x}{4} - 5 \cdot \frac{4}{4} - \frac{3}{4} < 1$

Combine $- 5$ and $\frac{4}{4}$ .

$\frac{15 x}{4} + \frac{- 5 \cdot 4}{4} - \frac{3}{4} < 1$

Combine the numerators over the common denominator.

$\frac{15 x}{4} + \frac{- 5 \cdot 4 - 3}{4} < 1$

Simplify the numerator.

Multiply $- 5$ by $4$ .

$\frac{15 x}{4} + \frac{- 20 - 3}{4} < 1$

Subtract $3$ from $- 20$ .

$\frac{15 x}{4} + \frac{- 23}{4} < 1$

Move the negative in front of the fraction.

$\frac{15 x}{4} - \frac{23}{4} < 1$

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

Add $\frac{23}{4}$ to both sides of the inequality.

$\frac{15 x}{4} < 1 + \frac{23}{4}$

Write $1$ as a fraction with a common denominator.

$\frac{15 x}{4} < \frac{4}{4} + \frac{23}{4}$

Combine the numerators over the common denominator.

$\frac{15 x}{4} < \frac{4 + 23}{4}$

Add $4$ and $23$ .

$\frac{15 x}{4} < \frac{27}{4}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$15 x < 27$

Divide each term in $15 x < 27$ by $15$ and simplify.

Divide each term in $15 x < 27$ by $15$ .

$\frac{15 x}{15} < \frac{27}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 x}{15} < \frac{27}{15}$

Divide $x$ by $1$ .

$x < \frac{27}{15}$

Simplify the right side.

Cancel the common factor of $27$ and $15$ .

Factor $3$ out of $27$ .

$x < \frac{3 (9)}{15}$

Cancel the common factors.

Factor $3$ out of $15$ .

$x < \frac{3 \cdot 9}{3 \cdot 5}$

Cancel the common factor.

$x < \frac{3 \cdot 9}{3 \cdot 5}$

Rewrite the expression.

$x < \frac{9}{5}$

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{9}{5}$

Interval Notation:

$(- \infty, \frac{9}{5})$

Solve the Inequality for x -5+3/4(5x-1)<1

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