Solve 4/3-2x-1/4geq1/2-3x+1/4

$$\frac { 4 } { 3 } - \frac { 2 x - 1 } { 4 } \geq \frac { 1 } { 2 } - \frac { 3 x + 1 } { 4 }$$

Solve for x

$$x\geq -\frac{16}{3}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,4,2. Since 12 is positive, the inequality direction remains the same.

$$16-3\left(2x-1\right)\geq 6-3\left(3x+1\right)$$

Use the distributive property to multiply -3 by 2x-1.

$$16-6x+3\geq 6-3\left(3x+1\right)$$

Add 16 and 3 to get 19.

$$19-6x\geq 6-3\left(3x+1\right)$$

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

$$19-6x\geq 6-9x-3$$

Subtract 3 from 6 to get 3.

$$19-6x\geq 3-9x$$

Add 9x to both sides.

$$19-6x+9x\geq 3$$

Combine -6x and 9x to get 3x.

$$19+3x\geq 3$$

Subtract 19 from both sides.

$$3x\geq 3-19$$

Subtract 19 from 3 to get -16.

$$3x\geq -16$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x\geq -\frac{16}{3}$$