About Equation Definition:
An equation is a mathematical statement where two algebraic expressions are set equal to each other. The solution to an equation is any value that makes the equation true when it replaces the variable. We can check any potential solutions with substitution.
Test Objectives
- Understand the difference between an expression and an equation
- Demonstrate the ability to evaluate an algebraic expression for a given value
- Demonstrate the ability to check a proposed solution for an equation
#1:
Instructions: Determine whether each is a solution to the given equation.
$$a)\hspace{.25em}\frac{b}{2}=-11$$$$\text{Check:}\hspace{.2em}{-}5, -22$$
$$b)\hspace{.25em}{-}301=-7(1 - 6a)$$$$\text{Check:}\hspace{.2em}{-}7,4$$
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#2:
Instructions: Determine whether each is a solution to the given equation.
$$a)\hspace{.25em}256=8(-7p + 4)$$$$\text{Check:}\hspace{.2em}0,-4$$
$$b)\hspace{.25em}\frac{1}{3x}- \frac{2}{3x^2}=\frac{1}{x^2}$$$$\text{Check:}\hspace{.2em}5,-6$$
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#3:
Instructions: Determine whether each is a solution to the given equation.
$$a)\hspace{.25em}x^2 + 7x=-10$$$$\text{Check:}\hspace{.2em}{-}5,0$$
$$b)\hspace{.25em}\frac{z}{20}=-18$$$$\text{Check:}\hspace{.2em}360, -1, -360$$
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#4:
Instructions: Determine whether each is a solution to the given equation.
$$a)\hspace{.25em}\frac{1}{2y}+ \frac{1}{2y^2}=\frac{1}{y}$$$$\text{Check:}\hspace{.2em}10, 1$$
$$b)\hspace{.25em}k^2 - 16k=-64$$$$\text{Check:}\hspace{.2em}3,8$$
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#5:
Instructions: Determine whether each is a solution to the given equation.
$$a)\hspace{.25em}x^2 - 15x=-56$$$$\text{Check:}\hspace{.2em}0,7$$
$$b)\hspace{.25em}8(4 - r) + 3=91$$$$\text{Check:}\hspace{.2em}{-}7,-4$$
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Written Solutions:
#1:
Solutions:
a) -5 no : -22 yes
b) -7 yes : 4 no
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#2:
Solutions:
a) 0 no : -4 yes
b) 5 yes : -6 no
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#3:
Solutions:
a) -5 yes : 0 no
b) 360 no : -1 no : -360 yes
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#4:
Solutions:
a) 10 no : 1 yes
b) 3 no : 8 yes
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#5:
Solutions:
a) 0 no : 7 yes
b) -7 yes : -4 no
