Solve 4(x+2)geq9x-1/2

$$4 ( x + 2 ) \geq \frac { 9 x - 1 } { 2 }$$

Solve for x

$$x\leq 17$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$8\left(x+2\right)\geq 9x-1$$

Use the distributive property to multiply 8 by x+2.

$$8x+16\geq 9x-1$$

Subtract 9x from both sides.

$$8x+16-9x\geq -1$$

Combine 8x and -9x to get -x.

$$-x+16\geq -1$$

Subtract 16 from both sides.

$$-x\geq -1-16$$

Subtract 16 from -1 to get -17.

$$-x\geq -17$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\leq \frac{-17}{-1}$$

Fraction \frac{-17}{-1} can be simplified to 17 by removing the negative sign from both the numerator and the denominator.

$$x\leq 17$$