Solving Equations & Inequalities Review

Front

What is the formula to find the total savings after a certain number of months if you start with an initial amount and save a fixed amount each month?

Back

Total Savings = Initial Amount + (Monthly Savings × Number of Months)

Front

If Savannah saves $165 per month and starts with $145, how much will she have after 13 months?

Back

Total Savings = 145 + (165 × 13) = $2,290

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that can satisfy the equation.

Front

What does it mean if an equation has infinitely many solutions?

Back

It means that any value for the variable will satisfy the equation.

Front

How do you solve the inequality 9 ≥ -2m + 2 - 3?

Back

First, simplify: 9 ≥ -2m - 1. Then, add 1 to both sides: 10 ≥ -2m. Finally, divide by -2 (remember to flip the inequality): m ≥ -5.

Front

What is the solution to the equation 2(9x – 6) = 6(3x – 2) + 2?

Back

This equation simplifies to 18x - 12 = 18x - 12, which has no solution because it is always true.

Front

What is the solution to the inequality -3 − 6(4x + 6) > -111?

Back

First, simplify: -3 - 24x - 36 > -111. Then, combine like terms: -24x > -72. Finally, divide by -24 (flip the inequality): x < 3.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

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 or less than another.

Front

What does it mean to isolate a variable in an equation?

Back

To isolate a variable means to manipulate the equation so that the variable is on one side and all other terms are on the other side.