Solve A=23*(a+b+c)-(a+b+c)

$$A = 23 \cdot ( a + b + c ) - ( a + b + c )$$

Solve for A

$$A=22\left(a+b+c\right)$$

Solution Steps

Use the distributive property to multiply 23 by a+b+c.

$$A=23a+23b+23c-\left(a+b+c\right)$$

To find the opposite of a+b+c, find the opposite of each term.

$$A=23a+23b+23c-a-b-c$$

Combine 23a and -a to get 22a.

$$A=22a+23b+23c-b-c$$

Combine 23b and -b to get 22b.

$$A=22a+22b+23c-c$$

Combine 23c and -c to get 22c.

$$A=22a+22b+22c$$

Solve for a

$$a=\frac{A-22b-22c}{22}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 23 by a+b+c.

$$A=23a+23b+23c-\left(a+b+c\right)$$

To find the opposite of a+b+c, find the opposite of each term.

$$A=23a+23b+23c-a-b-c$$

Combine 23a and -a to get 22a.

$$A=22a+23b+23c-b-c$$

Combine 23b and -b to get 22b.

$$A=22a+22b+23c-c$$

Combine 23c and -c to get 22c.

$$A=22a+22b+22c$$

Swap sides so that all variable terms are on the left hand side.

$$22a+22b+22c=A$$

Subtract 22b from both sides.

$$22a+22c=A-22b$$

Subtract 22c from both sides.

$$22a=A-22b-22c$$

Divide both sides by 22.

$$\frac{22a}{22}=\frac{A-22b-22c}{22}$$

Dividing by 22 undoes the multiplication by 22.

$$a=\frac{A-22b-22c}{22}$$

Divide A-22b-22c by 22.

$$a=\frac{A}{22}-b-c$$