Solve 5x/6-7/9leq2x-41/2

$$\frac{ 5x }{ 6 } - \frac{ 7 }{ 9 } \leq 2x-4 \frac{ 1 }{ 2 }$$

Solve for x

$$x\geq \frac{67}{21}$$

Solution Steps

Multiply both sides of the equation by 18, the least common multiple of 6,9,2. Since 18 is positive, the inequality direction remains the same.

$$3\times 5x-14\leq 36x-9\left(4\times 2+1\right)$$

Multiply 3 and 5 to get 15.

$$15x-14\leq 36x-9\left(4\times 2+1\right)$$

Multiply 4 and 2 to get 8.

$$15x-14\leq 36x-9\left(8+1\right)$$

Add 8 and 1 to get 9.

$$15x-14\leq 36x-9\times 9$$

Multiply -9 and 9 to get -81.

$$15x-14\leq 36x-81$$

Subtract 36x from both sides.

$$15x-14-36x\leq -81$$

Combine 15x and -36x to get -21x.

$$-21x-14\leq -81$$

Add 14 to both sides.

$$-21x\leq -81+14$$

Add -81 and 14 to get -67.

$$-21x\leq -67$$

Divide both sides by -21. Since -21 is negative, the inequality direction is changed.

$$x\geq \frac{-67}{-21}$$

Fraction \frac{-67}{-21} can be simplified to \frac{67}{21} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{67}{21}$$