Lesson 5

Steps in Solving Equations

Let’s recall steps in solving equations

Explain or show why each of these equations is equivalent to $7(x-15) + 3 = 8$ .

$7x - 105 + 3 = 8$
$7(x-15) - 5 = 0$
$7x - 102 - 8 = 0$

Here is Clare’s work to solve some equations. For each problem, do you agree or disagree with Clare’s work? Explain your reasoning.

$2(x-1)+4 = 3x - 2$
$2x - 2 + 4 = 3x - 2$
$2x + 2 = 3x - 2$
$2x = 3x$
$\text{-}x = 0$
$x = 0$
$3(x-1) = 5x + 6$
$3x - 1 = 5x + 6$
$\text{-}1 = 2x + 6$
$\text{-}7 = 2x$
$-3.5 = x$
$(x-2)(x+3) = x+10$
$x^2 + x - 6 =x + 10$
$x^2 - 6 = 10$
$x^2 = 16$
$x = 4$

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.
$(3x-5)(x-2) = 0$
- 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
$x(x-9) - 42 = 0$
- 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
$(x+12)(x-1) = 0$
- 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

Lesson 5

5.1: Explaining Equivalent Expressions

5.2: Checking Work

5.3: Row Game: Rewriting Equations

Summary