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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.

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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 $geq$ ).