Solve -5/8*a-3/4:41/2geq-51/8

$$- \frac { 5 } { 8 } \cdot a - \frac { 3 } { 4 } : 4 \frac { 1 } { 2 } \geq - 5 \frac { 1 } { 8 }$$

Solve for a

$$a\leq \frac{119}{15}$$

Solution Steps

Multiply both sides of the equation by 8. Since 8 is positive, the inequality direction remains the same.

$$-5a-\frac{16}{9}\times \frac{3}{4}\geq -\left(5\times 8+1\right)$$

Multiply -\frac{16}{9} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$-5a+\frac{-16\times 3}{9\times 4}\geq -\left(5\times 8+1\right)$$

Do the multiplications in the fraction \frac{-16\times 3}{9\times 4}.

$$-5a+\frac{-48}{36}\geq -\left(5\times 8+1\right)$$

Reduce the fraction \frac{-48}{36} to lowest terms by extracting and canceling out 12.

$$-5a-\frac{4}{3}\geq -\left(5\times 8+1\right)$$

Multiply 5 and 8 to get 40.

$$-5a-\frac{4}{3}\geq -\left(40+1\right)$$

Add 40 and 1 to get 41.

$$-5a-\frac{4}{3}\geq -41$$

Add \frac{4}{3} to both sides.

$$-5a\geq -41+\frac{4}{3}$$

Convert -41 to fraction -\frac{123}{3}.

$$-5a\geq -\frac{123}{3}+\frac{4}{3}$$

Since -\frac{123}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$-5a\geq \frac{-123+4}{3}$$

Add -123 and 4 to get -119.

$$-5a\geq -\frac{119}{3}$$

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

$$a\leq \frac{-\frac{119}{3}}{-5}$$

Express \frac{-\frac{119}{3}}{-5} as a single fraction.

$$a\leq \frac{-119}{3\left(-5\right)}$$

Multiply 3 and -5 to get -15.

$$a\leq \frac{-119}{-15}$$

Fraction \frac{-119}{-15} can be simplified to \frac{119}{15} by removing the negative sign from both the numerator and the denominator.

$$a\leq \frac{119}{15}$$