Solve for x 6(x+3)<=4x+1

$6 (x + 3) \leq 4 x + 1$

Step 1

Simplify $6 (x + 3)$ .

Rewrite.

$0 + 0 + 6 (x + 3) \leq 4 x + 1$

Simplify by adding zeros.

$6 (x + 3) \leq 4 x + 1$

Apply the distributive property.

$6 x + 6 \cdot 3 \leq 4 x + 1$

Multiply $6$ by $3$ .

$6 x + 18 \leq 4 x + 1$

Step 2

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

Subtract $4 x$ from both sides of the inequality.

$6 x + 18 - 4 x \leq 1$

Subtract $4 x$ from $6 x$ .

$2 x + 18 \leq 1$

Step 3

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

Subtract $18$ from both sides of the inequality.

$2 x \leq 1 - 18$

Subtract $18$ from $1$ .

$2 x \leq - 17$

Step 4

Divide each term in $2 x \leq - 17$ by $2$ and simplify.

Divide each term in $2 x \leq - 17$ by $2$ .

$\frac{2 x}{2} \leq \frac{- 17}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{- 17}{2}$

Divide $x$ by $1$ .

$x \leq \frac{- 17}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x \leq - \frac{17}{2}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq - \frac{17}{2}$

Interval Notation:

$(- \infty, - \frac{17}{2}]$