Solve (25/12-x)+41/9leq-17/36?

$$( 2 \frac { 5 } { 12 } - x ) + 4 \frac { 1 } { 9 } \leq - 1 \frac { 7 } { 36 } ?$$

Solve for x

$$x\geq \frac{139}{18}$$

Solution Steps

Multiply both sides of the equation by 36, the least common multiple of 12,9,36. Since 36 is positive, the inequality direction remains the same.

$$3\left(2\times 12+5\right)-36x+4\left(4\times 9+1\right)\leq -\left(1\times 36+7\right)$$

Multiply 2 and 12 to get 24.

$$3\left(24+5\right)-36x+4\left(4\times 9+1\right)\leq -\left(1\times 36+7\right)$$

Add 24 and 5 to get 29.

$$3\times 29-36x+4\left(4\times 9+1\right)\leq -\left(1\times 36+7\right)$$

Multiply 3 and 29 to get 87.

$$87-36x+4\left(4\times 9+1\right)\leq -\left(1\times 36+7\right)$$

Multiply 4 and 9 to get 36.

$$87-36x+4\left(36+1\right)\leq -\left(1\times 36+7\right)$$

Add 36 and 1 to get 37.

$$87-36x+4\times 37\leq -\left(1\times 36+7\right)$$

Multiply 4 and 37 to get 148.

$$87-36x+148\leq -\left(1\times 36+7\right)$$

Add 87 and 148 to get 235.

$$235-36x\leq -\left(1\times 36+7\right)$$

Multiply 1 and 36 to get 36.

$$235-36x\leq -\left(36+7\right)$$

Add 36 and 7 to get 43.

$$235-36x\leq -43$$

Subtract 235 from both sides.

$$-36x\leq -43-235$$

Subtract 235 from -43 to get -278.

$$-36x\leq -278$$

Divide both sides by -36. Since -36 is negative, the inequality direction is changed.

$$x\geq \frac{-278}{-36}$$

Reduce the fraction \frac{-278}{-36} to lowest terms by extracting and canceling out -2.

$$x\geq \frac{139}{18}$$