Lesson 5
Steps in Solving Equations
 Let’s recall steps in solving equations
5.1: Explaining Equivalent Expressions
Explain or show why each of these equations is equivalent to \(7(x15) + 3 = 8\).
 \(7x  105 + 3 = 8\)
 \(7(x15)  5 = 0\)
 \(7x  102  8 = 0\)
5.2: Checking Work
Here is Clare’s work to solve some equations. For each problem, do you agree or disagree with Clare’s work? Explain your reasoning.

\(2(x1)+4 = 3x  2\)
\(2x  2 + 4 = 3x  2\)
\(2x + 2 = 3x  2\)
\(2x = 3x\)
\(\text{}x = 0\)
\(x = 0\) 
\(3(x1) = 5x + 6\)
\(3x  1 = 5x + 6\)
\(\text{}1 = 2x + 6\)
\(\text{}7 = 2x\)
\(3.5 = x\) 
\((x2)(x+3) = x+10\)
\(x^2 + x  6 =x + 10 \)
\(x^2  6 = 10\)
\(x^2 = 16\)
\(x = 4\)
5.3: Row Game: Rewriting Equations
Work independently on your column. Partner A completes the questions in column A only and partner B completes the questions in column B only. Your answers in each row should match. Work on one row at a time and check if your answer matches your partner’s before moving on. If you don’t get the same answer, work together to find any mistakes.
Partner A: Write an equivalent equation so that the given condition is true.

\(5x+10 = 35\)

The expression on the right side is 0


\(x^2  9x = 42\)

The left side is a product


\(x(x+3) + 9 = 1\)

The right side is 0


\(8(x+1) = 5x\)

The left side is 0 and there are no parentheses


\(11+x = \frac{12}{x}\)

The equation is quadratic and the right side is zero.


\((3x5)(x2) = 0\)

One side of the equation has a term with \(3x^2\)


\(4x^2  4 = 8\)

The right side is 0 and the left side is a product

Partner B: Write an equivalent equation so that the given condition is true.

\(5(x+9) = 0\)

The left side is expressed as the sum of two terms


\(x(x9)  42 = 0\)

The left side is a product and the right side is not 0


\(x(x+3) + 6 = 2\)

The right side is 0


\(3x = 8\)

The left side is 0


\((x+12)(x1) = 0\)

The left side involves \(x^2\)


\(3x  11 = \frac{10}{x}\)

One side of the equation has a term with \(3x^2\)


\(4(x^2  1) = 8\)

The right side of is 0 and the left side is a product
