Solve |4*1+3*2+k|/sqrt{4^2+3^2}=3

$$\frac { | 4 \times 1 + 3 \times 2 + k | } { \sqrt { 4 ^ { 2 } + 3 ^ { 2 } } } = 3$$

Solve for k

$$k=-25$$

$$k=5$$

Steps Using Definition of Absolute Value

Multiply 4 and 1 to get 4. Multiply 3 and 2 to get 6.

$$\frac{|4+6+k|}{\sqrt{4^{2}+3^{2}}}=3$$

Add 4 and 6 to get 10.

$$\frac{|10+k|}{\sqrt{4^{2}+3^{2}}}=3$$

Calculate 4 to the power of 2 and get 16.

$$\frac{|10+k|}{\sqrt{16+3^{2}}}=3$$

Calculate 3 to the power of 2 and get 9.

$$\frac{|10+k|}{\sqrt{16+9}}=3$$

Add 16 and 9 to get 25.

$$\frac{|10+k|}{\sqrt{25}}=3$$

Calculate the square root of 25 and get 5.

$$\frac{|10+k|}{5}=3$$

Multiply both sides by 5.

$$|10+k|=3\times 5$$

Multiply 3 and 5 to get 15.

$$|10+k|=15$$

Combine like terms and use the properties of equality to get the variable on one side of the equal sign and the numbers on the other side. Remember to follow the order of operations.

$$|k+10|=15$$

Use the definition of absolute value.

$$k+10=15 k+10=-15$$

Subtract 10 from both sides of the equation.

$$k=5 k=-25$$