U1 8th Grade Review Solving Linear Equations and Inequalities

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

How do you solve a linear equation for x?

Back

To solve a linear equation for x, isolate x on one side of the equation by performing inverse operations on both sides.

Front

What is the solution to the equation 4x + 1 = 7x - 5?

Back

The solution is x = 2.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves representing the set of solutions on a number line or coordinate plane, using a solid line for 'greater than or equal to' and 'less than or equal to', and a dashed line for 'greater than' and 'less than'.

Front

How do you solve the inequality 7n - 1 > 76?

Back

To solve the inequality, add 1 to both sides to get 7n > 77, then divide by 7 to find n > 11.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation shows equality (e.g., 2x + 3 = 7), while a linear inequality shows a relationship of greater than or less than (e.g., 2x + 3 > 7).

Front

What does the solution x > -9 represent in the inequality -2(x + 2) < 14?

Back

The solution x > -9 indicates that any value greater than -9 satisfies the inequality.

Front

What is the first step in solving the inequality -2(x + 2) < 14?

Back

The first step is to distribute -2 to both terms inside the parentheses, resulting in -2x - 4 < 14.

Front

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

Back

Checking your solution ensures that the values you found satisfy the original inequality, confirming that your solution is correct.

Front

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

Back

Isolating a variable means rearranging the equation so that the variable is on one side by itself, making it easier to solve.