Solve 2(x-1)/2-2x+1/3geq7

$$\frac { 2 ( x - 1 ) } { 2 } - \frac { 2 x + 1 } { 3 } \geq 7$$

Solve for x

$$x\geq 25$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

$$3\times 2\left(x-1\right)-2\left(2x+1\right)\geq 42$$

Multiply 3 and 2 to get 6.

$$6\left(x-1\right)-2\left(2x+1\right)\geq 42$$

Use the distributive property to multiply 6 by x-1.

$$6x-6-2\left(2x+1\right)\geq 42$$

Use the distributive property to multiply -2 by 2x+1.

$$6x-6-4x-2\geq 42$$

Combine 6x and -4x to get 2x.

$$2x-6-2\geq 42$$

Subtract 2 from -6 to get -8.

$$2x-8\geq 42$$

Add 8 to both sides.

$$2x\geq 42+8$$

Add 42 and 8 to get 50.

$$2x\geq 50$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x\geq \frac{50}{2}$$

Divide 50 by 2 to get 25.

$$x\geq 25$$