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How do you translate 'A company must produce at least 500 units' into an inequality?
$x \geq 500$, where $x$ is the number of units.
How do you translate 'The maximum weight limit is 50 pounds' into an inequality?
$w \leq 50$, where $w$ is the weight.
How do you translate 'Fuel efficiency should be greater than 30 miles per gallon' into an inequality?
$e > 30$, where $e$ is the fuel efficiency.
How do you translate 'The temperature must remain below 32°F' into an inequality?
$t < 32$, where $t$ is the temperature.
A factory's cost is $5x + 1000$ and revenue is $8x$. How do you set up the inequality to find when the factory makes a profit?
Profit occurs when revenue > cost: $8x > 5x + 1000$.
A car rental costs $40 per day plus $0.25 per mile. How do you represent the total cost for 3 days if 'm' is the number of miles?
Total cost: $40(3) + 0.25m$.
How do you solve the inequality $2x + 5 < 11$?
Subtract 5 from both sides: $2x < 6$. Divide by 2: $x < 3$.
How do you solve the inequality $-3x \geq 12$?
Divide both sides by -3 and flip the sign: $x \leq -4$.
How do you represent the solution $x > 5$ on a number line?
Draw a number line with an open circle at 5 and shade to the right.
How do you represent the solution $x \leq -2$ on a number line?
Draw a number line with a closed circle at -2 and shade to the left.
What does 'at least' translate to in inequality symbols?
Greater than or equal to: $\geq$
What does 'at most' translate to in inequality symbols?
Less than or equal to: $\leq$
What does 'more than' translate to in inequality symbols?
Greater than: $>$
What does 'less than' translate to in inequality symbols?
Less than: $<$
What is a linear inequality?
A mathematical statement showing the relationship between two expressions that are not equal.
What is the solution to a linear inequality?
A range of values that make the inequality true.
What is the first step in solving a linear inequality?
Isolate the variable on one side of the inequality.
What must you do when multiplying/dividing by a negative number in an inequality?
Reverse the inequality sign.
What does an open circle on a number line represent when graphing inequalities?
The endpoint is *not* included in the solution ($<$ or $>$).
What does a closed circle on a number line represent when graphing inequalities?
The endpoint *is* included in the solution ($leq$ or $geq$).