Solve 0.5x+1.2(360-5x/10)leq40

$$0.5x+1.2( \frac{ 360-5x }{ 10 } ) \leq 40$$

Solve for x

$$x\geq 32$$

Solution Steps

Multiply both sides of the equation by 10. Since 10 is positive, the inequality direction remains the same.

$$5x+1.2\left(360-5x\right)\leq 400$$

Use the distributive property to multiply 1.2 by 360-5x.

$$5x+432-6x\leq 400$$

Combine 5x and -6x to get -x.

$$-x+432\leq 400$$

Subtract 432 from both sides.

$$-x\leq 400-432$$

Subtract 432 from 400 to get -32.

$$-x\leq -32$$

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

$$x\geq \frac{-32}{-1}$$

Fraction \frac{-32}{-1} can be simplified to 32 by removing the negative sign from both the numerator and the denominator.

$$x\geq 32$$