Solve for x -4x+1>=7

$- 4 x + 1 \geq 7$

Step 1

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

Subtract $1$ from both sides of the inequality.

$- 4 x \geq 7 - 1$

Subtract $1$ from $7$ .

$- 4 x \geq 6$

Step 2

Divide each term in $- 4 x \geq 6$ by $- 4$ and simplify.

Divide each term in $- 4 x \geq 6$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} \leq \frac{6}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \leq \frac{6}{- 4}$

Divide $x$ by $1$ .

$x \leq \frac{6}{- 4}$

Simplify the right side.

Cancel the common factor of $6$ and $- 4$ .

Factor $2$ out of $6$ .

$x \leq \frac{2 (3)}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 3

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(- \infty, - \frac{3}{2}]$

Solve for x -4x+1>=7

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