# Solve linear equation and check: 7x+3=6(x-1)+9

Linear equations and graphs

Solve linear equation and check: $$7x+3=6(x-1)+9$$

2021-01-03

Apply the distributive property to the right side of the equation as shown on the board
$$a(b-c)=a\times b-a\times c$$
$$7x+3=6(x-1)+9$$
$$\Rightarrow7x+3=(6)(x)-(6)(1)+9$$
$$\displaystyle\Rightarrow{7}{x}+{3}={6}{x}-{6}+{9}$$
Evaluate the constant terms on the right side as shown on the board
$$7x+3=6x+3$$
Subtract 3 from both sides as shown on the board
$$7x+3-3=6x+3-3$$
Cancelling out +3 and -3 from both sides, we get the equation as shown on the board
$$7x=6x$$
Subtract 6x from both sides as shown on the board
$$7x-6x=6x-6x$$
Cancelling out 6x and -6x from the right side we get the equation as shown on the board
$$7x-6x=0$$
Subtracting 6x from 7x on the left side we get the final value of x as shown on the board
$$x=0$$
$$x=0$$