Solve the Inequality for x (4x+6)/7<2

$\frac{4 x + 6}{7} < 2$

Multiply both sides by $7$ .

$\frac{4 x + 6}{7} \cdot 7 < 2 \cdot 7$

Simplify.

Simplify the left side.

Simplify $\frac{4 x + 6}{7} \cdot 7$ .

Factor $2$ out of $4 x + 6$ .

Factor $2$ out of $4 x$ .

$\frac{2 (2 x) + 6}{7} \cdot 7 < 2 \cdot 7$

Factor $2$ out of $6$ .

$\frac{2 (2 x) + 2 (3)}{7} \cdot 7 < 2 \cdot 7$

Factor $2$ out of $2 (2 x) + 2 (3)$ .

$\frac{2 (2 x + 3)}{7} \cdot 7 < 2 \cdot 7$

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{2 (2 x + 3)}{7} \cdot 7 < 2 \cdot 7$

Rewrite the expression.

$2 (2 x + 3) < 2 \cdot 7$

Apply the distributive property.

$2 (2 x) + 2 \cdot 3 < 2 \cdot 7$

Multiply.

Multiply $2$ by $2$ .

$4 x + 2 \cdot 3 < 2 \cdot 7$

Multiply $2$ by $3$ .

$4 x + 6 < 2 \cdot 7$

Simplify the right side.

Multiply $2$ by $7$ .

$4 x + 6 < 14$

Solve for $x$ .

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

Subtract $6$ from both sides of the inequality.

$4 x < 14 - 6$

Subtract $6$ from $14$ .

$4 x < 8$

Divide each term in $4 x < 8$ by $4$ and simplify.

Divide each term in $4 x < 8$ by $4$ .

$\frac{4 x}{4} < \frac{8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} < \frac{8}{4}$

Divide $x$ by $1$ .

$x < \frac{8}{4}$

Simplify the right side.

Divide $8$ by $4$ .

$x < 2$

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$

Solve the Inequality for x (4x+6)/7<2

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