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

Question
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*b-a*c
7x+3=6(x-1)+9
$$\displaystyle\Rightarrow{7}{x}+{3}={\left(^\right)}{\left({x}\right)}-{\left({6}\right)}{\left({1}\right)}+{9}$$
$$\displaystyle\Rightarrow{7}{x}+{3}={6}{x}-{6}+{9}$$
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

### Relevant Questions

Given linear equation y = 6 − 7x
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.
We give linear equations. For each equation,
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation. y=6-7x
What would be the linear equation for this function, & the graph?
$$\displaystyle{\left({X}_{{1}},{Y}_{{1}}\right)}={\left({4},{8}\right)},{\left({X}_{{2}},{Y}_{{2}}\right)}={\left({6},-{9}\right)}$$
[Table]
A real-estate agent is trying to determine the relationship between the distance a 3-bedroom home is from New York City and its average selling price. He records the data for 6 homes shown below.
Equation:
Approximate cost of home 90 miles from NYC?
What would be the linear equation for this function, & the graph?
$$\displaystyle{\left({X}_{{1}},{Y}_{{1}}\right)}={\left(-{7},{3}\right)},{\left({X}_{{2}},{Y}_{{2}}\right)}={\left({6},{3}\right)}$$
What would be the linear equation for this function, & the graph??
$$\displaystyle{\left({X}_{{1}},{Y}_{{1}}\right)}={\left({3},{6}\right)},{\left({X}_{{2}},{Y}_{{2}}\right)}={\left({3},-{5}\right)}$$
Which equation does not represent a line with an x-intercept of 3?
(A) y=−2x+6
(B) y=−13x+1
(C) y=23x−2
(D) y=3x−1
The graph shows the number of teaspoons of lemon juice in cups of lemonade.
Which ordered pair represents a ratio equivalent to the ratio of teaspoons of lemon juice to cups of lemonade shown by the point on the graph?
A. (4,16)
B. (6,1)
C. (9,3)
D. (16,4)
Oscar chose A as the correct answer. How did he get that answer?
$$\displaystyle{Y}={6}-\frac{{2}}{{{3}{x}}}$$
$$\displaystyle{Y}={x}+{1}$$