Solutions and Equations

Mrs. Waller was asked to solve the equation -2(x-1)=15. Her steps are shown below:

Step 1: -2x+2=15
Step 2: -2x=17
Step 3: x=-8.5

Which statement about her solution is correct?

• The problem is worked out correctly at each step.

• In Step 1, the problem should be -2x-2=15.

• In Step 2, the problem should be -2x=13.

• In step 3, the answer should be x=19.

Solve the equation for x: -2\left(x-7\right)+3x=7x+13-6x

• x+14=x+13 or 14=13, so there's no solution.

• x=-\frac{1}{4} , so there's one solution.

• x+5=x+13 or 5=13, so there's no solution.

• x=-\frac{1}{2} , so there's one solution.

Part 1: Michelle had $400 in her savings account at the beginning of the summer. Each week she took $20 out of her account. Skyler had $120 in his account at the beginning of the summer. Each week he added $36 to his account. In which week will Michelle and Skyler have the same amount of money in their accounts? Show all work and write your answer in a sentence. Write an equation that represents the situation where w represents the number of weeks.

Part 2: Michelle had $400 in her savings account at the beginning of the summer. Each week she took $20 out of her account. Skyler had $120 in his account at the beginning of the summer. Each week he added $36 to his account. In which week will Michelle and Skyler have the same amount of money in their accounts? Show all work and write your answer in a sentence.

• w=3

• w=5

• w=7

• w=10

Part 3: Michelle had $400 in her savings account at the beginning of the summer. Each week she took $20 out of her account. Skyler had $120 in his account at the beginning of the summer. Each week he added $36 to his account. In which week will Michelle and Skyler have the same amount of money in their accounts? Show all work and write your answer in a sentence.

• Michelle and Skyler will have $5 in their accounts.

• 5 weeks.

• Michelle and Skyler will have the same amount of money in their accounts after 5 weeks.

• Michelle and Skyler will have $5 in their accounts after 5 weeks.

How many solutions does the following equation have?

• one solution

• infinitely many solutions

• no solution

How many solutions does the following equation have?

• one solution

• infinitely many solutions

• no solution

How many solutions does the following equation have?

• one solution

• infinitely many solutions

• no solution

How many solutions does the following equation have?

• one solution

• infinitely many solutions

• no solution

How many solutions does the following equation have?

• one solution

• infinitely many solutions

• no solution