Solve x/60+3.5(1-x/160+1-x/30)leq64

$$\frac { x } { 60 } + 3.5 ( \frac { 1 - x } { 160 } + \frac { 1 - x } { 30 } ) \leq 64$$

Solve for x

$$x\geq -\frac{61307}{117}$$

Solution Steps

Multiply both sides of the equation by 480, the least common multiple of 60,160,30. Since 480 is positive, the inequality direction remains the same.

$$8x+1680\left(\frac{1-x}{160}+\frac{1-x}{30}\right)\leq 30720$$

Combine \frac{1-x}{160} and \frac{1-x}{30} to get \frac{19}{480}\left(1-x\right).

$$8x+1680\times \frac{19}{480}\left(1-x\right)\leq 30720$$

Use the distributive property to multiply \frac{19}{480} by 1-x.

$$8x+1680\left(\frac{19}{480}+\frac{19}{480}\left(-1\right)x\right)\leq 30720$$

Multiply \frac{19}{480} and -1 to get -\frac{19}{480}.

$$8x+1680\left(\frac{19}{480}-\frac{19}{480}x\right)\leq 30720$$

Use the distributive property to multiply 1680 by \frac{19}{480}-\frac{19}{480}x.

$$8x+1680\times \frac{19}{480}+1680\left(-\frac{19}{480}\right)x\leq 30720$$

Express 1680\times \frac{19}{480} as a single fraction.

$$8x+\frac{1680\times 19}{480}+1680\left(-\frac{19}{480}\right)x\leq 30720$$

Multiply 1680 and 19 to get 31920.

$$8x+\frac{31920}{480}+1680\left(-\frac{19}{480}\right)x\leq 30720$$

Reduce the fraction \frac{31920}{480} to lowest terms by extracting and canceling out 240.

$$8x+\frac{133}{2}+1680\left(-\frac{19}{480}\right)x\leq 30720$$

Express 1680\left(-\frac{19}{480}\right) as a single fraction.

$$8x+\frac{133}{2}+\frac{1680\left(-19\right)}{480}x\leq 30720$$

Multiply 1680 and -19 to get -31920.

$$8x+\frac{133}{2}+\frac{-31920}{480}x\leq 30720$$

Reduce the fraction \frac{-31920}{480} to lowest terms by extracting and canceling out 240.

$$8x+\frac{133}{2}-\frac{133}{2}x\leq 30720$$

Combine 8x and -\frac{133}{2}x to get -\frac{117}{2}x.

$$-\frac{117}{2}x+\frac{133}{2}\leq 30720$$

Subtract \frac{133}{2} from both sides.

$$-\frac{117}{2}x\leq 30720-\frac{133}{2}$$

Convert 30720 to fraction \frac{61440}{2}.

$$-\frac{117}{2}x\leq \frac{61440}{2}-\frac{133}{2}$$

Since \frac{61440}{2} and \frac{133}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{117}{2}x\leq \frac{61440-133}{2}$$

Subtract 133 from 61440 to get 61307.

$$-\frac{117}{2}x\leq \frac{61307}{2}$$

Multiply both sides by -\frac{2}{117}, the reciprocal of -\frac{117}{2}. Since -\frac{117}{2} is negative, the inequality direction is changed.

$$x\geq \frac{61307}{2}\left(-\frac{2}{117}\right)$$

Multiply \frac{61307}{2} times -\frac{2}{117} by multiplying numerator times numerator and denominator times denominator.

$$x\geq \frac{61307\left(-2\right)}{2\times 117}$$

Do the multiplications in the fraction \frac{61307\left(-2\right)}{2\times 117}.

$$x\geq \frac{-122614}{234}$$

Reduce the fraction \frac{-122614}{234} to lowest terms by extracting and canceling out 2.

$$x\geq -\frac{61307}{117}$$