Solve 45x:(-9)geq35/10

$$45 x : ( - 9 ) \geq 3 \frac { 5 } { 10 }$$

Solve for x

$$x\leq -\frac{7}{10}$$

Solution Steps

Multiply both sides of the equation by 90, the least common multiple of -9,10. Since 90 is positive, the inequality direction remains the same.

$$-10\times 45x\geq 9\left(3\times 10+5\right)$$

Multiply -10 and 45 to get -450.

$$-450x\geq 9\left(3\times 10+5\right)$$

Multiply 3 and 10 to get 30.

$$-450x\geq 9\left(30+5\right)$$

Add 30 and 5 to get 35.

$$-450x\geq 9\times 35$$

Multiply 9 and 35 to get 315.

$$-450x\geq 315$$

Divide both sides by -450. Since -450 is negative, the inequality direction is changed.

$$x\leq \frac{315}{-450}$$

Reduce the fraction \frac{315}{-450} to lowest terms by extracting and canceling out 45.

$$x\leq -\frac{7}{10}$$