Algebra 1 RQ 2

Front

What is the solution to the inequality \( \frac{x}{8} > 4 \)?

Back

To solve for x, multiply both sides by 8: \( x > 32 \).

Front

What does the equation \( 250 + 65x = 575 \) represent in a real-world context?

Back

Mia is traveling to a location that is 575 miles away. She has already traveled 250 miles. The variable x represents the number of hours she needs to travel at a speed of 65 miles per hour.

Front

How do you solve the equation \( 2x + 5 = -17 \)?

Back

Subtract 5 from both sides: \( 2x = -22 \). Then divide by 2: \( x = -11 \).

Front

What is the solution to the inequality \( \frac{t}{10} - 7 < -1 \)?

Back

To solve for t, add 7 to both sides: \( \frac{t}{10} < 6 \). Then multiply by 10: \( t < 60 \).

Front

What inequality represents the maximum weight a truck can carry if it is loaded with a piano weighing 400 pounds and boxes weighing 50 pounds each?

Back

The inequality is \( 50x + 400 \leq 1600 \), where x is the number of boxes.

Front

What is the first step in solving a linear inequality?

Back

Identify the inequality symbol and isolate the variable on one side of the inequality.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

How do you graph the solution to an inequality?

Back

Use a number line to represent the variable, and use an open circle for < or > and a closed circle for ≤ or ≥.

Front

What does it mean to solve for a variable in an equation?

Back

It means to isolate the variable on one side of the equation to find its value.

Front

What is the importance of checking your solution in an inequality?

Back

Checking your solution ensures that it satisfies the original inequality and helps avoid mistakes.