Solve 5x-2/8-4x+1/6leqx+3/18

$$\frac { 5 x - 2 } { 8 } - \frac { 4 x + 1 } { 6 } \leq \frac { x + 3 } { 18 }$$

Solve for x

$$x\geq -6$$

Solution Steps

Multiply both sides of the equation by 72, the least common multiple of 8,6,18. Since 72 is positive, the inequality direction remains the same.

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

Use the distributive property to multiply 9 by 5x-2.

$$45x-18-12\left(4x+1\right)\leq 4\left(x+3\right)$$

Use the distributive property to multiply -12 by 4x+1.

$$45x-18-48x-12\leq 4\left(x+3\right)$$

Combine 45x and -48x to get -3x.

$$-3x-18-12\leq 4\left(x+3\right)$$

Subtract 12 from -18 to get -30.

$$-3x-30\leq 4\left(x+3\right)$$

Use the distributive property to multiply 4 by x+3.

$$-3x-30\leq 4x+12$$

Subtract 4x from both sides.

$$-3x-30-4x\leq 12$$

Combine -3x and -4x to get -7x.

$$-7x-30\leq 12$$

Add 30 to both sides.

$$-7x\leq 12+30$$

Add 12 and 30 to get 42.

$$-7x\leq 42$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x\geq \frac{42}{-7}$$

Divide 42 by -7 to get -6.

$$x\geq -6$$