Solve 2left(2x-1right)geq7left(x+1right)

$$2 \left( 2x-1 \right) \geq 7 \left( x+1 \right)$$

Solve for x

$$x\leq -3$$

Solution Steps

Use the distributive property to multiply 2 by 2x-1.

$$4x-2\geq 7\left(x+1\right)$$

Use the distributive property to multiply 7 by x+1.

$$4x-2\geq 7x+7$$

Subtract 7x from both sides.

$$4x-2-7x\geq 7$$

Combine 4x and -7x to get -3x.

$$-3x-2\geq 7$$

Add 2 to both sides.

$$-3x\geq 7+2$$

Add 7 and 2 to get 9.

$$-3x\geq 9$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x\leq \frac{9}{-3}$$

Divide 9 by -3 to get -3.

$$x\leq -3$$