Question

name: aaliyah equavce
trying more two - step equations
date: 10 - 9 2075 period: 1 2 3 4 5 6 7
solve each equation, showing all algebraic steps. verify your solution by checking algebraically.

1. - 40 = 8(g - 11)

8g - 88=-40
8g = 48
8g/8 = 48/8
g = 6

1. 3/2w + 5=-7

3/2w=-12
w=-8

1. 0.4h - 5.3 = 4.7

0.4h = 10
0.4h/0.4 = 10/0.4
h = 25

1. 0.75x + 1.5=-3

0.75x=-4.5
0.75x/0.75=-4.5/0.75
x=-6

1. 2(x + 4)-3 = 13

2x+8 - 3 = 13
2x + 5 = 13
2x = 8
2x/2 = 8/2
x = 4

1. x/4 - 2 = 3

the model represents an equation.
which of the following represents the equation and its solution?
a. 3x + 5 = 7
x = 2
b. 3x - 5 = 7
x = 4
c. - 5x + 3 = 7
x=-4
d. 3x - 5 = 7
x = 12
key: black square=-1, white square = + 1, black rectangle=-x, white rectangle = + x

Explanation:

Step1: Analyze left - hand side of equation

Count the number of positive $x$ terms and negative unit terms. There are 3 positive $x$ terms and 5 negative unit terms, so the left - hand side is $3x - 5$.

Step2: Analyze right - hand side of equation

Count the number of positive unit terms on the right - hand side. There are 7 positive unit terms, so the right - hand side is 7. The equation is $3x - 5=7$.

Step3: Solve the equation

Add 5 to both sides: $3x-5 + 5=7 + 5$, which simplifies to $3x=12$. Then divide both sides by 3: $\frac{3x}{3}=\frac{12}{3}$, so $x = 4$.

Answer:

B. $3x - 5 = 7$, $x = 4$