Solve 4-x/2+1>6x-7/3

$$\frac { 4 - x } { 2 } + 1 > \frac { 6 x - 7 } { 3 }$$

Solve for x

$$x<\frac{32}{15}$$

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.

$$3\left(4-x\right)+6>2\left(6x-7\right)$$

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

$$12-3x+6>2\left(6x-7\right)$$

Add 12 and 6 to get 18.

$$18-3x>2\left(6x-7\right)$$

Use the distributive property to multiply 2 by 6x-7.

$$18-3x>12x-14$$

Subtract 12x from both sides.

$$18-3x-12x>-14$$

Combine -3x and -12x to get -15x.

$$18-15x>-14$$

Subtract 18 from both sides.

$$-15x>-14-18$$

Subtract 18 from -14 to get -32.

$$-15x>-32$$

Divide both sides by -15. Since -15 is negative, the inequality direction is changed.

$$x<\frac{-32}{-15}$$

Fraction \frac{-32}{-15} can be simplified to \frac{32}{15} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{32}{15}$$