Inequalities and Point-Slope Form

Front

What is an inequality?

Back

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

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What is point-slope form of a linear equation?

Back

Point-slope form is given by the equation y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

Front

How do you determine if a circle is colored in for the inequality 5 ≥ x?

Back

The circle is colored in because the inequality includes 'greater than or equal to', indicating that the endpoint is included.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you solve the inequality 4(x - 3) ≤ 8x - 4?

Back

Distributing gives 4x - 12 ≤ 8x - 4. Rearranging leads to -12 + 4 ≤ 8x - 4x, resulting in x ≥ -2.

Front

What does it mean if x > -7 in an inequality?

Back

It means that x can take any value greater than -7, but not -7 itself.

Front

What is the first step in solving the inequality -8(x - 3) - 4x < 108?

Back

First, distribute -8 to get -8x + 24 - 4x < 108.

Front

What is the solution to the inequality x ≥ -2?

Back

The solution indicates that x can be any value greater than or equal to -2.

Front

How do you convert from point-slope form to slope-intercept form?

Back

To convert, solve for y in the equation y - y₁ = m(x - x₁) to get y = mx + (y₁ - mx₁).