Solve the Inequality for x (4x+2)/5<=2

$\frac{4 x + 2}{5} \leq 2$

Step 1

Multiply both sides by $5$ .

$\frac{4 x + 2}{5} \cdot 5 \leq 2 \cdot 5$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{4 x + 2}{5} \cdot 5$ .

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

Factor $2$ out of $4 x$ .

$\frac{2 (2 x) + 2}{5} \cdot 5 \leq 2 \cdot 5$

Factor $2$ out of $2$ .

$\frac{2 (2 x) + 2 (1)}{5} \cdot 5 \leq 2 \cdot 5$

Factor $2$ out of $2 (2 x) + 2 (1)$ .

$\frac{2 (2 x + 1)}{5} \cdot 5 \leq 2 \cdot 5$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 (2 x + 1)}{5} \cdot 5 \leq 2 \cdot 5$

Rewrite the expression.

$2 (2 x + 1) \leq 2 \cdot 5$

Apply the distributive property.

$2 (2 x) + 2 \cdot 1 \leq 2 \cdot 5$

Multiply.

Multiply $2$ by $2$ .

$4 x + 2 \cdot 1 \leq 2 \cdot 5$

Multiply $2$ by $1$ .

$4 x + 2 \leq 2 \cdot 5$

Simplify the right side.

Multiply $2$ by $5$ .

$4 x + 2 \leq 10$

Step 3

Solve for $x$ .

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

Subtract $2$ from both sides of the inequality.

$4 x \leq 10 - 2$

Subtract $2$ from $10$ .

$4 x \leq 8$

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

Divide each term in $4 x \leq 8$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $8$ by $4$ .

$x \leq 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 2$

Interval Notation:

$(- \infty, 2]$

Solve the Inequality for x (4x+2)/5<=2

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