Solve 2*(x+2)geq7*(x-2)+2

$$2 \cdot ( x + 2 ) \geq 7 \cdot ( x - 2 ) + 2$$

Solve for x

$$x\leq \frac{16}{5}$$

Solution Steps

Use the distributive property to multiply 2 by x+2.

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

Use the distributive property to multiply 7 by x-2.

$$2x+4\geq 7x-14+2$$

Add -14 and 2 to get -12.

$$2x+4\geq 7x-12$$

Subtract 7x from both sides.

$$2x+4-7x\geq -12$$

Combine 2x and -7x to get -5x.

$$-5x+4\geq -12$$

Subtract 4 from both sides.

$$-5x\geq -12-4$$

Subtract 4 from -12 to get -16.

$$-5x\geq -16$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\leq \frac{-16}{-5}$$

Fraction \frac{-16}{-5} can be simplified to \frac{16}{5} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{16}{5}$$