Solve 3x-5/3+4x-3/6-6x-2/9geq71/18

$$\frac { 3 x - 5 } { 3 } + \frac { 4 x - 3 } { 6 } - \frac { 6 x - 2 } { 9 } \geq 7 \frac { 1 } { 18 }$$

Solve for x

$$x\geq 9$$

Solution Steps

Multiply both sides of the equation by 18, the least common multiple of 3,6,9,18. Since 18 is positive, the inequality direction remains the same.

$$6\left(3x-5\right)+3\left(4x-3\right)-2\left(6x-2\right)\geq 7\times 18+1$$

Use the distributive property to multiply 6 by 3x-5.

$$18x-30+3\left(4x-3\right)-2\left(6x-2\right)\geq 7\times 18+1$$

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

$$18x-30+12x-9-2\left(6x-2\right)\geq 7\times 18+1$$

Combine 18x and 12x to get 30x.

$$30x-30-9-2\left(6x-2\right)\geq 7\times 18+1$$

Subtract 9 from -30 to get -39.

$$30x-39-2\left(6x-2\right)\geq 7\times 18+1$$

Use the distributive property to multiply -2 by 6x-2.

$$30x-39-12x+4\geq 7\times 18+1$$

Combine 30x and -12x to get 18x.

$$18x-39+4\geq 7\times 18+1$$

Add -39 and 4 to get -35.

$$18x-35\geq 7\times 18+1$$

Multiply 7 and 18 to get 126.

$$18x-35\geq 126+1$$

Add 126 and 1 to get 127.

$$18x-35\geq 127$$

Add 35 to both sides.

$$18x\geq 127+35$$

Add 127 and 35 to get 162.

$$18x\geq 162$$

Divide both sides by 18. Since 18 is positive, the inequality direction remains the same.

$$x\geq \frac{162}{18}$$

Divide 162 by 18 to get 9.

$$x\geq 9$$