Solve 1-2x/3+1/2geq3x/2-4/3=

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

Solve for x

$$x\leq \frac{17}{13}$$

Solution Steps

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

$$6-2\times 2x+3\geq 3\times 3x-8$$

Multiply -2 and 2 to get -4.

$$6-4x+3\geq 3\times 3x-8$$

Add 6 and 3 to get 9.

$$9-4x\geq 3\times 3x-8$$

Multiply 3 and 3 to get 9.

$$9-4x\geq 9x-8$$

Subtract 9x from both sides.

$$9-4x-9x\geq -8$$

Combine -4x and -9x to get -13x.

$$9-13x\geq -8$$

Subtract 9 from both sides.

$$-13x\geq -8-9$$

Subtract 9 from -8 to get -17.

$$-13x\geq -17$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x\leq \frac{-17}{-13}$$

Fraction \frac{-17}{-13} can be simplified to \frac{17}{13} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{17}{13}$$