Solve the Inequality for x 3/7(35x-14)<=(21x)/2+3

$\frac{3}{7} (35 x - 14) \leq \frac{21 x}{2} + 3$

Simplify $\frac{3}{7} \cdot (35 x - 14)$ .

Rewrite.

$0 + 0 + \frac{3}{7} \cdot (35 x - 14) \leq \frac{21 x}{2} + 3$

Simplify by adding zeros.

$\frac{3}{7} \cdot (35 x - 14) \leq \frac{21 x}{2} + 3$

Apply the distributive property.

$\frac{3}{7} (35 x) + \frac{3}{7} \cdot - 14 \leq \frac{21 x}{2} + 3$

Cancel the common factor of $7$ .

Factor $7$ out of $35 x$ .

$\frac{3}{7} (7 (5 x)) + \frac{3}{7} \cdot - 14 \leq \frac{21 x}{2} + 3$

Cancel the common factor.

$\frac{3}{7} (7 (5 x)) + \frac{3}{7} \cdot - 14 \leq \frac{21 x}{2} + 3$

Rewrite the expression.

$3 (5 x) + \frac{3}{7} \cdot - 14 \leq \frac{21 x}{2} + 3$

Multiply $5$ by $3$ .

$15 x + \frac{3}{7} \cdot - 14 \leq \frac{21 x}{2} + 3$

Cancel the common factor of $7$ .

Factor $7$ out of $- 14$ .

$15 x + \frac{3}{7} \cdot (7 (- 2)) \leq \frac{21 x}{2} + 3$

Cancel the common factor.

$15 x + \frac{3}{7} \cdot (7 \cdot - 2) \leq \frac{21 x}{2} + 3$

Rewrite the expression.

$15 x + 3 \cdot - 2 \leq \frac{21 x}{2} + 3$

Multiply $3$ by $- 2$ .

$15 x - 6 \leq \frac{21 x}{2} + 3$

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

Subtract $\frac{21 x}{2}$ from both sides of the inequality.

$15 x - 6 - \frac{21 x}{2} \leq 3$

To write $15 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$15 x \cdot \frac{2}{2} - \frac{21 x}{2} - 6 \leq 3$

Combine $15 x$ and $\frac{2}{2}$ .

$\frac{15 x \cdot 2}{2} - \frac{21 x}{2} - 6 \leq 3$

Combine the numerators over the common denominator.

$\frac{15 x \cdot 2 - 21 x}{2} - 6 \leq 3$

Simplify the numerator.

Factor $3 x$ out of $15 x \cdot 2 - 21 x$ .

Factor $3 x$ out of $15 x \cdot 2$ .

$\frac{3 x (5 \cdot 2) - 21 x}{2} - 6 \leq 3$

Factor $3 x$ out of $- 21 x$ .

$\frac{3 x (5 \cdot 2) + 3 x (- 7)}{2} - 6 \leq 3$

Factor $3 x$ out of $3 x (5 \cdot 2) + 3 x (- 7)$ .

$\frac{3 x (5 \cdot 2 - 7)}{2} - 6 \leq 3$

Multiply $5$ by $2$ .

$\frac{3 x (10 - 7)}{2} - 6 \leq 3$

Subtract $7$ from $10$ .

$\frac{3 x \cdot 3}{2} - 6 \leq 3$

Multiply $3$ by $3$ .

$\frac{9 x}{2} - 6 \leq 3$

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

Add $6$ to both sides of the inequality.

$\frac{9 x}{2} \leq 3 + 6$

Add $3$ and $6$ .

$\frac{9 x}{2} \leq 9$

Multiply both sides by $2$ .

$\frac{9 x}{2} \cdot 2 \leq 9 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{9 x}{2} \cdot 2 \leq 9 \cdot 2$

Rewrite the expression.

$9 x \leq 9 \cdot 2$

Simplify the right side.

Multiply $9$ by $2$ .

$9 x \leq 18$

Divide each term in $9 x \leq 18$ by $9$ and simplify.

Divide each term in $9 x \leq 18$ by $9$ .

$\frac{9 x}{9} \leq \frac{18}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} \leq \frac{18}{9}$

Divide $x$ by $1$ .

$x \leq \frac{18}{9}$

Simplify the right side.

Divide $18$ by $9$ .

$x \leq 2$

The result can be shown in multiple forms.

Inequality Form:

$x \leq 2$

Interval Notation:

$(- \infty, 2]$

Solve the Inequality for x 3/7(35x-14)<=(21x)/2+3

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