Solve 7x/6+-5x-4/14leq1+3x/7-2-4x/2

$$\frac { 7 x } { 6 } + \frac { - 5 x - 4 } { 14 } \leq \frac { 1 + 3 x } { 7 } - \frac { 2 - 4 x } { 2 }$$

Solve for x

$$x\geq \frac{6}{17}$$

Solution Steps

Multiply both sides of the equation by 42, the least common multiple of 6,14,7,2. Since 42 is positive, the inequality direction remains the same.

$$7\times 7x+3\left(-5x-4\right)\leq 6\left(1+3x\right)-21\left(2-4x\right)$$

Multiply 7 and 7 to get 49.

$$49x+3\left(-5x-4\right)\leq 6\left(1+3x\right)-21\left(2-4x\right)$$

Use the distributive property to multiply 3 by -5x-4.

$$49x-15x-12\leq 6\left(1+3x\right)-21\left(2-4x\right)$$

Combine 49x and -15x to get 34x.

$$34x-12\leq 6\left(1+3x\right)-21\left(2-4x\right)$$

Use the distributive property to multiply 6 by 1+3x.

$$34x-12\leq 6+18x-21\left(2-4x\right)$$

Use the distributive property to multiply -21 by 2-4x.

$$34x-12\leq 6+18x-42+84x$$

Subtract 42 from 6 to get -36.

$$34x-12\leq -36+18x+84x$$

Combine 18x and 84x to get 102x.

$$34x-12\leq -36+102x$$

Subtract 102x from both sides.

$$34x-12-102x\leq -36$$

Combine 34x and -102x to get -68x.

$$-68x-12\leq -36$$

Add 12 to both sides.

$$-68x\leq -36+12$$

Add -36 and 12 to get -24.

$$-68x\leq -24$$

Divide both sides by -68. Since -68 is negative, the inequality direction is changed.

$$x\geq \frac{-24}{-68}$$

Reduce the fraction \frac{-24}{-68} to lowest terms by extracting and canceling out -4.

$$x\geq \frac{6}{17}$$