Question

odd one out
in each box, circle the one which does not belong with the group. provide a justification for why you select the problem that does not fit with the others.
a. nima will spend less than $5
b.
c. \\( \frac { 1 } { 2 } x + 1 0 \geq 1 1. 5 \\)
a. demick ran at least 30 miles last week
b. demick plans to run 150 miles in 2 months. how many miles should he run each month to reach his goal?
c. \\( 1 5 0 < 2 x \\)
a.
b. emily needs no more than $60 to buy the tv she wants.
c. \\( 2 x + 2 0 \geq 1 4 0 \\)
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Explanation:

• First Box:
• Option A is a statement about spending less than a certain amount.
• Option B is a number line representation (which is a visual way to show inequalities).
• Option C is an inequality equation.
• Option A is the odd one out because it is a simple statement without any mathematical symbol (like in an inequality equation or a number - line representation which is a visual for an inequality).
• Second Box:
• Option A is a statement about running at least (an inequality concept: \(x\geq30\)).
• Option B is a question about an equation (to find a value, \(150 = 2x\)).
• Option C is an inequality (\(150<2x\)).
• Option B is the odd one out as it is about an equation (finding an exact value) while A and C are related to inequalities.
• Third Box:
• Option A is a number - line representation (visual for an inequality, \(x\geq60\)).
• Option B is a statement about needing no more than (an inequality concept: \(x\leq60\)).
• Option C is an inequality equation (\(2x + 20\geq140\) simplifies to \(x\geq60\)).
• Option B is the odd one out. While A and C are representations (visual and algebraic) of the inequality \(x\geq60\), B is a statement of \(x\leq60\) (opposite in the sense of the direction of the inequality when compared to A and C's underlying inequality after simplification).

Answer:

• First Box: A. Nima will spend less than $5$ is the odd one out. It is a simple statement, while B (number - line for \(x\geq\frac{1}{2}\)) and C (\(\frac{1}{2}x + 10\geq11.5\)) are related to inequality representations (visual and algebraic).
• Second Box: B. Demick plans to run 150 miles in 2 months. How many miles should he run each month to reach his goal? is the odd one out. It is about an equation (\(150 = 2x\)), while A (\(x\geq30\)) and C (\(150<2x\)) are inequalities.
• Third Box: B. Emily needs no more than $60$ to buy the TV she wants is the odd one out. A (number - line for \(x\geq60\)) and C (\(2x + 20\geq140\) or \(x\geq60\)) are about \(x\geq60\), while B is about \(x\leq60\).