Solve for x (x-8)/4<=(x-4)/6+1/12

$\frac{x - 8}{4} \leq \frac{x - 4}{6} + \frac{1}{12}$

Step 1

Multiply both sides by $4$ .

$\frac{x - 8}{4} \cdot 4 \leq (\frac{x - 4}{6} + \frac{1}{12}) \cdot 4$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{x - 8}{4} \cdot 4 \leq (\frac{x - 4}{6} + \frac{1}{12}) \cdot 4$

Rewrite the expression.

$x - 8 \leq (\frac{x - 4}{6} + \frac{1}{12}) \cdot 4$

Simplify the right side.

Simplify $(\frac{x - 4}{6} + \frac{1}{12}) \cdot 4$ .

To write $\frac{x - 4}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x - 8 \leq (\frac{x - 4}{6} \cdot \frac{2}{2} + \frac{1}{12}) \cdot 4$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x - 4}{6}$ by $\frac{2}{2}$ .

$x - 8 \leq (\frac{(x - 4) \cdot 2}{6 \cdot 2} + \frac{1}{12}) \cdot 4$

Multiply $6$ by $2$ .

$x - 8 \leq (\frac{(x - 4) \cdot 2}{12} + \frac{1}{12}) \cdot 4$

Combine the numerators over the common denominator.

$x - 8 \leq \frac{(x - 4) \cdot 2 + 1}{12} \cdot 4$

Simplify the numerator.

Apply the distributive property.

$x - 8 \leq \frac{x \cdot 2 - 4 \cdot 2 + 1}{12} \cdot 4$

Move $2$ to the left of $x$ .

$x - 8 \leq \frac{2 \cdot x - 4 \cdot 2 + 1}{12} \cdot 4$

Multiply $- 4$ by $2$ .

$x - 8 \leq \frac{2 \cdot x - 8 + 1}{12} \cdot 4$

Add $- 8$ and $1$ .

$x - 8 \leq \frac{2 x - 7}{12} \cdot 4$

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$x - 8 \leq \frac{2 x - 7}{4 (3)} \cdot 4$

Cancel the common factor.

$x - 8 \leq \frac{2 x - 7}{4 \cdot 3} \cdot 4$

Rewrite the expression.

$x - 8 \leq \frac{2 x - 7}{3}$

Step 3

Solve for $x$ .

Multiply both sides by $3$ .

$(x - 8) \cdot 3 \leq \frac{2 x - 7}{3} \cdot 3$

Simplify.

Simplify the left side.

Simplify $(x - 8) \cdot 3$ .

Apply the distributive property.

$x \cdot 3 - 8 \cdot 3 \leq \frac{2 x - 7}{3} \cdot 3$

Simplify the expression.

Move $3$ to the left of $x$ .

$3 \cdot x - 8 \cdot 3 \leq \frac{2 x - 7}{3} \cdot 3$

Multiply $- 8$ by $3$ .

$3 x - 24 \leq \frac{2 x - 7}{3} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 x - 24 \leq \frac{2 x - 7}{3} \cdot 3$

Rewrite the expression.

$3 x - 24 \leq 2 x - 7$

Solve for $x$ .

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

Subtract $2 x$ from both sides of the inequality.

$3 x - 24 - 2 x \leq - 7$

Subtract $2 x$ from $3 x$ .

$x - 24 \leq - 7$

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

Add $24$ to both sides of the inequality.

$x \leq - 7 + 24$

Add $- 7$ and $24$ .

$x \leq 17$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 17$

Interval Notation:

$(- \infty, 17]$

Solve for x (x-8)/4<=(x-4)/6+1/12

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