Solve 2k-(k-3)+4leq3k

$$2 k - ( k - 3 ) + 4 \leq 3 k$$

Solve for k

$$k\geq \frac{7}{2}$$

Solution Steps

To find the opposite of k-3, find the opposite of each term.

$$2k-k-\left(-3\right)+4\leq 3k$$

The opposite of -3 is 3.

$$2k-k+3+4\leq 3k$$

Combine 2k and -k to get k.

$$k+3+4\leq 3k$$

Add 3 and 4 to get 7.

$$k+7\leq 3k$$

Subtract 3k from both sides.

$$k+7-3k\leq 0$$

Combine k and -3k to get -2k.

$$-2k+7\leq 0$$

Subtract 7 from both sides. Anything subtracted from zero gives its negation.

$$-2k\leq -7$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$k\geq \frac{-7}{-2}$$

Fraction \frac{-7}{-2} can be simplified to \frac{7}{2} by removing the negative sign from both the numerator and the denominator.

$$k\geq \frac{7}{2}$$