Solve left(7left(-2-kright)+5left(k-(-2)right)+3left(-2-1right)right)=0

$$\left( 7 \left( -2-k \right) +5 \left( k-(-2) \right) +3 \left( -2-1 \right) \right) = 0$$

Solve for k

$$k = -\frac{13}{2} = -6\frac{1}{2} = -6.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by -2-k.

$$-14-7k+5\left(k-\left(-2\right)\right)+3\left(-2-1\right)=0$$

The opposite of -2 is 2.

$$-14-7k+5\left(k+2\right)+3\left(-2-1\right)=0$$

Use the distributive property to multiply 5 by k+2.

$$-14-7k+5k+10+3\left(-2-1\right)=0$$

Combine -7k and 5k to get -2k.

$$-14-2k+10+3\left(-2-1\right)=0$$

Add -14 and 10 to get -4.

$$-4-2k+3\left(-2-1\right)=0$$

Subtract 1 from -2 to get -3.

$$-4-2k+3\left(-3\right)=0$$

Multiply 3 and -3 to get -9.

$$-4-2k-9=0$$

Subtract 9 from -4 to get -13.

$$-13-2k=0$$

Add 13 to both sides. Anything plus zero gives itself.

$$-2k=13$$

Divide both sides by -2.

$$k=\frac{13}{-2}$$

Fraction \frac{13}{-2} can be rewritten as -\frac{13}{2} by extracting the negative sign.

$$k=-\frac{13}{2}$$