Question

I) For each equation, decide on a strategy to solve it and explain why you chose that strategy.

ii) Use your strategy to solve the equation. When appropriate, leave your
answer in simplest radical form.
a) 2x² - 3x = x² + 7x
b) 4x² + 6x + 1 = 0
c) x² + 4x - 3 = 0
d) (x + 3)² = - 2x
e) 3x² – 5x = 2x² + 4x + 10
f) 2(x + 3)(x -4) = 6x + 6

Answer 1

The equations are solved using various strategies such as combining like terms, factoring, quadratic formula, and rewriting equations.

Step-by-step explanation:

For the given equations:

a) 2x² - 3x = x² + 7x
Use the strategy of combining like terms and isolating variables to solve this equation.

b) 4x² + 6x + 1 = 0
Use the quadratic formula to solve this equation.

c) x² + 4x - 3 = 0
Use factoring to solve this equation.

d) (x + 3)² = - 2x
Rewrite the equation as a quadratic equation and then solve it.

e) 3x² – 5x = 2x² + 4x + 10
Use the strategy of combining like terms and isolating variables to solve this equation.

f) 2(x + 3)(x -4) = 6x + 6
Distribute and combine like terms to simplify the equation and then solve it.