Solve for x 6x>=3+4(2x-1)

$6 x \geq 3 + 4 (2 x - 1)$

Step 1

Simplify $3 + 4 (2 x - 1)$ .

Simplify each term.

Apply the distributive property.

$6 x \geq 3 + 4 (2 x) + 4 \cdot - 1$

Multiply $2$ by $4$ .

$6 x \geq 3 + 8 x + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$6 x \geq 3 + 8 x - 4$

Subtract $4$ from $3$ .

$6 x \geq 8 x - 1$

Step 2

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

Subtract $8 x$ from both sides of the inequality.

$6 x - 8 x \geq - 1$

Subtract $8 x$ from $6 x$ .

$- 2 x \geq - 1$

Step 3

Divide each term in $- 2 x \geq - 1$ by $- 2$ and simplify.

Divide each term in $- 2 x \geq - 1$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \leq \frac{- 1}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \leq \frac{- 1}{- 2}$

Divide $x$ by $1$ .

$x \leq \frac{- 1}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x \leq \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{1}{2}$

Interval Notation:

$(- \infty, \frac{1}{2}]$

Solve for x 6x>=3+4(2x-1)

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