Solve -23x+3/7+x-7/2leq-4

$$- \frac { 23 x + 3 } { 7 } + \frac { x - 7 } { 2 } \leq - 4$$

Solve for x

$$x\geq \frac{1}{39}$$

Solution Steps

Multiply both sides of the equation by 14, the least common multiple of 7,2. Since 14 is positive, the inequality direction remains the same.

$$-2\left(23x+3\right)+7\left(x-7\right)\leq -56$$

Use the distributive property to multiply -2 by 23x+3.

$$-46x-6+7\left(x-7\right)\leq -56$$

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

$$-46x-6+7x-49\leq -56$$

Combine -46x and 7x to get -39x.

$$-39x-6-49\leq -56$$

Subtract 49 from -6 to get -55.

$$-39x-55\leq -56$$

Add 55 to both sides.

$$-39x\leq -56+55$$

Add -56 and 55 to get -1.

$$-39x\leq -1$$

Divide both sides by -39. Since -39 is negative, the inequality direction is changed.

$$x\geq \frac{-1}{-39}$$

Fraction \frac{-1}{-39} can be simplified to \frac{1}{39} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{1}{39}$$