Question

lesson 7 practice problems

1. match each equation with an equivalent equation. some of the answer choices are not used.

a. 3x + 6 = 4x + 7
b. 3(x + 6) = 4x + 7
c. 4x + 3x = 7 - 6

1. 9x = 4x + 7
2. 3x + 18 = 4x + 7
3. 3x = 4x + 7
4. 3x - 1 = 4x
5. 7x = 1
6. mai says that equations a and b have the same solution.

equation a: -3(x + 7) = 24
equation b: x + 7 = -8
which statement explains why this is true?
a. adding 3 to both sides of equation a gives x + 7 = -8.
b. applying the distributive property to equation a gives x + 7 = -8.
c. subtracting 3 from both sides of equation a gives x + 7 = -8.
d. dividing both sides of equation a by -3 gives x + 7 = -8.

1. is 0 a solution to 2x + 10 = 4x + 10? explain or show your reasoning.

Explanation:

Step1: Simplify the left - hand side of option B in the first question

Expand $3(x + 6)$ using the distributive property $a(b + c)=ab+ac$. So, $3(x + 6)=3x+18$. So, the equation $3(x + 6)=4x + 7$ is equivalent to $3x + 18=4x + 7$.

Step2: Solve the second - question

Given Equation A: $-3(x + 7)=24$. Divide both sides of Equation A by $- 3$. We get $\frac{-3(x + 7)}{-3}=\frac{24}{-3}$, which simplifies to $x + 7=-8$. So, the correct option for the second question is D.

Step3: Check if 0 is a solution for the third - question

Substitute $x = 0$ into the equation $2x+10 = 4x+10$.
Left - hand side: When $x = 0$, $2(0)+10=10$.
Right - hand side: When $x = 0$, $4(0)+10=10$. Since the left - hand side equals the right - hand side when $x = 0$, 0 is a solution.

Answer:

1. B corresponds to $3x + 18=4x + 7$
2. D. Dividing both sides of Equation A by -3 gives $x + 7=-8$.
3. Yes. When $x = 0$, the left - hand side $2x+10=2(0)+10 = 10$ and the right - hand side $4x+10=4(0)+10 = 10$.